@unpublished{AlsaedyTarkhanov2016,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Hilbert boundary value problem for generalised Cauchy-Riemann equations},
  volume    = {5},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86109},
  pages     = {21},
  year      = {2016},
  abstract  = {We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.},
  language  = {en}
}
@article{LyTarkhanov2016,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for p-harmonic functions},
  series = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  volume    = {22},
  journal   = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-016-0109-7},
  pages     = {461 -- 472},
  year      = {2016},
  abstract  = {Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.},
  language  = {en}
}
@article{BaerStrohmaier2016,
  author    = {B{\"a}r, Christian and Strohmaier, Alexander},
  title     = {A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds},
  series = {Communications in mathematical physics},
  volume    = {347},
  journal   = {Communications in mathematical physics},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-016-2664-1},
  pages     = {703 -- 721},
  year      = {2016},
  abstract  = {We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.},
  language  = {en}
}
@article{HermannHumbert2016,
  author    = {Hermann, Andreas and Humbert, Emmanuel},
  title     = {About the mass of certain second order elliptic operators},
  series = {Advances in mathematics},
  volume    = {294},
  journal   = {Advances in mathematics},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0001-8708},
  doi       = {10.1016/j.aim.2016.03.008},
  pages     = {596 -- 633},
  year      = {2016},
  abstract  = {Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@article{KleinRosenberger2016,
  author    = {Klein, Markus and Rosenberger, Elke},
  title     = {Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators},
  series = {Asymptotic analysis},
  volume    = {97},
  journal   = {Asymptotic analysis},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0921-7134},
  doi       = {10.3233/ASY-151343},
  pages     = {61 -- 89},
  year      = {2016},
  abstract  = {We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and epsilon is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted l(2)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2016,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {An open mapping theorem for the Navier-Stokes equations},
  volume    = {5},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98687},
  pages     = {80},
  year      = {2016},
  abstract  = {We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed H{\"o}lder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fr{\´e}chet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of H{\"o}lder spaces.},
  language  = {en}
}
@article{BomansonJanhunenSchaubetal.2016,
  author    = {Bomanson, Jori and Janhunen, Tomi and Schaub, Torsten H. and Gebser, Martin and Kaufmann, Benjamin},
  title     = {Answer Set Programming Modulo Acyclicity},
  series = {Fundamenta informaticae},
  volume    = {147},
  journal   = {Fundamenta informaticae},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0169-2968},
  doi       = {10.3233/FI-2016-1398},
  pages     = {63 -- 91},
  year      = {2016},
  abstract  = {Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving.},
  language  = {en}
}
@article{FladHarutyunyanSchulze2016,
  author    = {Flad, H. -J. and Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotic parametrices of elliptic edge operators},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {7},
  journal   = {Journal of pseudo-differential operators and applications},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-016-0159-7},
  pages     = {321 -- 363},
  year      = {2016},
  abstract  = {We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.},
  language  = {en}
}
@article{AntoniniAzzaliSkandalis2016,
  author    = {Antonini, Paolo and Azzali, Sara and Skandalis, Georges},
  title     = {Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations},
  series = {Journal of functional analysis},
  volume    = {270},
  journal   = {Journal of functional analysis},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2015.06.017},
  pages     = {447 -- 481},
  year      = {2016},
  abstract  = {We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2016,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems for elliptic complexes},
  volume    = {5},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86705},
  pages     = {12},
  year      = {2016},
  abstract  = {The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.},
  language  = {en}
}