TY - INPR A1 - Yihong, Du A1 - Li, Ma T1 - Some remarks related to De Giorgi's conjecture N2 - For several classes of functions including the special case f(u) = u − u³, we obtain boundedness and symmetry results for solutions of the problem −Δu = f(u) defined on R up(n). Our results complement a number of recent results related to a conjecture of De Giorgi. T3 - Preprint - (2001) 18 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26027 ER - TY - INPR A1 - Yagdjian, Karen T1 - Geometric optics for the nonlinear hyperbolic systems of Kirchhoff-type N2 - Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations T3 - Preprint - (2001) 22 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26059 ER - TY - BOOK A1 - Yagdjian, Karen T1 - Geometric optics for the nonlinear hyperbolic systems of kirchhoff-type T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Xiaochun, Liu A1 - Witt, Ingo T1 - Asymptotic expansions for bounded solutions to semilinear Fuchsian equations N2 - It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions. T3 - Preprint - (2001) 01 KW - Calculus of conormal symbols KW - conormal asymptotic expansions KW - discrete saymptotic types KW - weighted Sobolev spaces with discrete saymptotics Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25912 ER - TY - INPR A1 - Witt, Ingo T1 - Asymptotic algebras N2 - The concept of asymptotic type that primarily appears in singular and asymptotic analysis is developed. Especially, asymptotic algebras are introduced. T3 - Preprint - (2001) 23 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26069 ER - TY - BOOK A1 - Witt, Ingo T1 - Asymptotic algebras T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels N2 - Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A. T3 - Preprint - (2001) 26 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26095 ER - TY - BOOK A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - The edge algebra structure of boundary value problems N2 - Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols. T3 - Preprint - (2001) 11 KW - Boundary value problems KW - pseudodifferential operators Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25955 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - The edge algebra structure of boundary value problems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER -