@unpublished{XiaochunWitt2002,
  author    = {Xiaochun, Liu and Witt, Ingo},
  title     = {Pseudodifferential calculi on the half-line respecting prescribed asymptotic types},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26255},
  year      = {2002},
  abstract  = {Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus},
  language  = {en}
}
@unpublished{Tarkhanov2002,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Anisotropic edge problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26280},
  year      = {2002},
  abstract  = {We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability.},
  language  = {en}
}
@unpublished{Witt2002,
  author    = {Witt, Ingo},
  title     = {A calculus for a class of finitely degenerate pseudodifferential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26246},
  year      = {2002},
  abstract  = {For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.},
  language  = {en}
}
@unpublished{LiuYangLu2002,
  author    = {Liu, Weian and Yang, Yin and Lu, Gang},
  title     = {Viscosity solutions of fully nonlinear parabolic systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26215},
  year      = {2002},
  abstract  = {In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].},
  language  = {en}
}
@unpublished{Krainer2002,
  author    = {Krainer, Thomas},
  title     = {On the inverse of parabolic boundary value problems for large times},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26310},
  year      = {2002},
  abstract  = {We construct algebras of Volterra pseudodifferential operators that contain, in particular, the inverses of the most natural classical systems of parabolic boundary value problems of general form. Parabolicity is determined by the invertibility of the principal symbols, and as a result is equivalent to the invertibility of the operators within the calculus. Existence, uniqueness, regularity, and asymptotics of solutions as t → ∞ are consquences of the mapping properties of the operators in exponentially weighted Sobolev spaces and subspaces with asymptotics. An important aspect of this work is that the microlocal and global kernel structure of the inverse operator (solution operator) of a parabolic boundary value problem for large times is clarified. Moreover, our approach naturally yields qualitative pertubation results for the solvability theory of parabolic boundary value problems. To achieve these results, we assign t = ∞ the meaning of a conical point and treat the operators as totally characteristic pseudodifferential boundary value problems.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin2002,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {Relative elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26400},
  year      = {2002},
  abstract  = {This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms.},
  language  = {en}
}
@unpublished{Davis2002,
  author    = {Davis, Simon},
  title     = {On the absence of large-order divergences in superstring theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26452},
  year      = {2002},
  abstract  = {The genus-dependence of multi-loop superstring ams is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string pertubation theory, a result which is based only on the supersymmetric generalization of the polyakov measure and not the gauge group of the string model.},
  language  = {en}
}
@unpublished{SchroheSeiler2002,
  author    = {Schrohe, Elmar and Seiler, J{\"o}rg},
  title     = {The resolvent of closed extensions of cone differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26378},
  year      = {2002},
  abstract  = {We study an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A )-¹ exists in a sector of the complex plane and decays like 1/|λ| as |λ| -> ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with striaght conical degeneracy and establish maximal regularity for the Cauchy problem u - Δu = f, u(0) = 0.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov2002,
  author    = {Kytmanov, Alexander and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Holomorphic Lefschetz formula for manifolds with boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26354},
  year      = {2002},
  abstract  = {The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M -> M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschtz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschtz formula on a compact complex manifold with boundary},
  language  = {en}
}
@unpublished{HuichengWitt2002,
  author    = {Huicheng, Yin and Witt, Ingo},
  title     = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26395},
  year      = {2002},
  language  = {en}
}
@unpublished{Paneah2002,
  author    = {Paneah, Boris},
  title     = {Dynamic methods in the general theory of cauchy type functional equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26295},
  year      = {2002},
  abstract  = {Contents: 1 Introduction. Denfitions and Discussions 2 Solvability of the Cauchy Type Functional Equations 2.1 The Case of a P-configuration 2.2 The Case of a Z-configuration 2.3 Multiplicative Cauchy type functional equations 3 Problems in Analysis Reducing to Cauchy Type Functional Equations 3.1 Some problems in Integral Geometry and Cauchy Functional Equations 3.2 First Boundary Problem for Hyperbolic Differential Equations and Cauchy Type Functional Equations 4 Functional Equations Determining Polynomials},
  language  = {en}
}
@unpublished{Krainer2002,
  author    = {Krainer, Thomas},
  title     = {On the calculus of pseudodifferential operators with an anisotropic analytic parameter},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26200},
  year      = {2002},
  abstract  = {We introduce the Volterra calculus of pseudodifferential operators with an anisotropic analytic parameter based on "twisted" operator-valued Volterra symbols. We establish the properties of the symbolic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side. In particular, we investigate the kernel cut-off operator via direct oscillatory integral techniques purely on symbolic level. We discuss the notion of parabolic for the calculus of Volterra operators, and construct Volterra parametrices for parabolic operators within the calculus.},
  language  = {en}
}
@unpublished{Davis2002,
  author    = {Davis, Simon},
  title     = {Connections and generalized gauge transformations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26468},
  year      = {2002},
  abstract  = {The derivation of the standard model from a higher-dimensional action suggests a further study of the fibre bundle formulation of gauge theories to determine the variations in the choice of structure group that are allowed in this geometrical setting. The action of transformations on the projection of fibres to their submanifolds are characteristic of theories with fewer gauge vector bosons, and specific examples are given, which may have phenomenological relevance. The spinor space for the three generations of fermions in the standard model is described algebraically.},
  language  = {en}
}
@unpublished{Davis2002,
  author    = {Davis, Simon},
  title     = {On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26474},
  year      = {2002},
  abstract  = {The Goldbach partitions of an even number greater than 2, given by the sums of two prime addends, form the non-empty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. The proof depends on contour arguments for complex functions in the unit disk.},
  language  = {en}
}
@unpublished{Yin2002,
  author    = {Yin, Huicheng},
  title     = {Formation and construction of a shock wave for 3-D compressible Euler equations with spherical initial data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26263},
  year      = {2002},
  abstract  = {In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point.},
  language  = {en}
}
@unpublished{Yin2002,
  author    = {Yin, Huicheng},
  title     = {Global existence of a shock for the supersonic flow past a curved wedge},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26272},
  year      = {2002},
  abstract  = {This note is devoted to the study on the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, wwe show that a shock attached at the wedge will exist globally.},
  language  = {en}
}
@unpublished{Witt2002,
  author    = {Witt, Ingo},
  title     = {Local asymptotic types},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26346},
  year      = {2002},
  abstract  = {The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG-SIGAL's theory of the inversion of finitely meromorphic, operator-valued functions at a point.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2002,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Surgery and the relative index theorem for families of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26300},
  year      = {2002},
  abstract  = {We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2002,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotics and relative index on a cylinder with conical cross section},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26446},
  year      = {2002},
  abstract  = {We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26327},
  year      = {2002},
  abstract  = {We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.},
  language  = {en}
}
@unpublished{ManicciaSchulze2002,
  author    = {Maniccia, L. and Schulze, Bert-Wolfgang},
  title     = {An algebra of meromorphic corner symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26360},
  year      = {2002},
  abstract  = {Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.},
  language  = {en}
}
@unpublished{OliaroSchulze2002,
  author    = {Oliaro, Alessandro and Schulze, Bert-Wolfgang},
  title     = {Parameter-dependent boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26424},
  year      = {2002},
  abstract  = {As is known from Kondratyev's work, boundary value problems for elliptic operators on a manifold with conical singularities and boundary are controlled by a principal symbolic hierarchy, where the conormal symbols belong to the typical new components, compared with the smooth case, with interior and boundary symbols. A similar picture may be expected on manifolds with corners when the base of the cone itself is a manifold with conical or edge singularities. This is a natural situation in a number of applications, though with essential new difficulties. We investigate here corresponding conormal symbols in terms of a calculus of holomorphic parameter-dependent edge boundary value problems on the base. We show that a certain kernel cut-off procedure generates all such holomorphic families, modulo smoothing elements, and we establish conormal symbols as an algebra as is necessary for a parametrix constructions in the elliptic case.},
  language  = {en}
}
@unpublished{CoriascoSchulze2002,
  author    = {Coriasco, Sandro and Schulze, Bert-Wolfgang},
  title     = {Edge problems on configurations with model cones of different dimensions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26438},
  year      = {2002},
  abstract  = {Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here, edges. Starting from edge-degenerate operators on Wj, j = 1, ..., N, we construct an algebra with extra "transmission" conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator-valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.},
  language  = {en}
}
@unpublished{SchulzeSeiler2002,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Pseudodifferential boundary value problems with global projection conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26233},
  year      = {2002},
  abstract  = {Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26386},
  year      = {2002},
  abstract  = {When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2002,
  author    = {Harutjunjan, G. and Schulze, Bert-Wolfgang},
  title     = {Reduction of orders in boundary value problems without the transmission property},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26220},
  year      = {2002},
  abstract  = {Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We consider smooth symbols and ellipticity without additional boundary conditions which is the relevant case on a manifold with boundary. Starting from a class of symbols that has been investigated before for integer orders in boundary value problems with the transmission property we study operators of arbitrary real orders that play a similar role for operators without the transmission property. Moreover, we show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We finally investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26415},
  year      = {2002},
  abstract  = {The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26335},
  year      = {2002},
  abstract  = {Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.},
  language  = {en}
}