The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems.
type: Item
instance of: scholarly article
title: The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems.
zbMATH Open document ID: 1126.35368
DOI: 10.1007/BF01198487
author: W. L. Wendland
author: Roland Duduchava
published in: Integral Equations and Operator Theory
publication date: 1995-11-29T00:00:00Z
review text: The paper presents general results on Fredholmness and solvability in Bessel potential and Besov spaces for systems of pseudodifferential equations on a compact domain with smooth boundary, based on a refined Wiener-Hopf factorization technique. This developes the method suggested by \textit{G. Eskin} [Boundary value problem for elliptic pseudodifferential equations, AMS Translations of Mathematical Monographs 52 (1981; Zbl 0458.35002)] for scalar pseudodifferential equations with ``constant coefficients''. Furthermore, the Wiener-Hopf method is applied to the boundary integral equations corresponding to the Dirichlet and Neumann problems for an anisotropic medium, yielding short proofs for solvability and regularity results by Duduchava, Natroshvili and Shargorodsky. Finally, new results on the asymptotic behaviour of solutions to crack problems are given, which improve even those for the isotropic case obtained by \textit{M. Costabel} and \textit{E. P. Stephan} [Integral Equations Oper. Theory 10, 467--504 (1987; Zbl 0632.73091)].
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 821683
zbMATH Keywords: pseudodifferential equations
zbMATH Keywords: Wiener-Hopf method
zbMATH Keywords: anisotropic elasticity
zbMATH Keywords: asymptotics of solutions
reviewed by: Johannes Elschner
MaRDI profile type: Publication
cites work: Regularization in 3D for anisotropic elastodynamic crack and obstacle problems
cites work: Q3468659
cites work: Boundary problems for pseudo-differential operators
cites work: General edge asymptotics of solutions of second-order elliptic boundary value problems I
cites work: An improved boundary element Galerkin method for three-dimensional crack problems
cites work: Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
cites work: Q3322630
cites work: Q3866607
cites work: Q4711922
cites work: Q4782327
cites work: Q4698929
cites work: Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary
cites work: Q3907885
cites work: Q3470840
cites work: Functional calculus of pseudo-differential boundary problems
cites work: Pseudo-differential boundary problems in Lp, spaces
cites work: On the Dirichlet problem in elasticity for a domain exterior to an arc
cites work: Q3026487
cites work: Q5589570
cites work: Q3811802
cites work: On stress singularities near the boundary of a polygonal crack
cites work: Reduction of order for pseudodifferential operators on lipschitz domains
cites work: Q3733265
cites work: On a Problem of BABUŠKA (Stable Asymptotics of the Solution to the DIRICHLET Problem for Elliptic Equations of Second Order in Domains with Angular Points)
cites work: Q3251655
cites work: Boundary integral equations for mixed Dirichlet, Neumann and transmission problems
cites work: Q4740221
cites work: Three‐dimensional singularities of elastic fields near vertices
cites work: Bessel Potential Operators for Canonical Lipschitz Domains
cites work: Q5557123
cites work: A remark on Mikhlin-Hörmander multipliers theorem
cites work: Elliptic Systems of Singular Integral Operators. I. The Half-Space Case
cites work: Some Remarks on the Boundedness of Pseudodifferential Operators
cites work: FACTORIZATION OF PARAMETER-DEPENDENT MATRIX-FUNCTIONS IN NORMED RINGS AND CERTAIN RELATED QUESTIONS IN THE THEORY OF NOETHERIAN OPERATORS
cites work: Q5607484
cites work: A hypersingular boundary integral method for two-dimensional screen and crack problems
cites work: The boundary element method for three-dimensional Stokes flows exterior to an open surface
full work available at URL: https://doi.org/10.1007/bf01198487
OpenAlex ID: W2070363367
description: scientific article; zbMATH DE number 821683