Dirichlet Problems in Polyhedral Domains I: Regularity of the Solutions

DOI10.1002/mana.19941680115zbMath0844.35014OpenAlexW2033717992MaRDI QIDQ4845820

Serge Nicaise, Jean M.-S. Lubuma

Publication date: 29 August 1996

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19941680115

zbMATH Keywords

weighted Sobolev spacespolyhedral domains

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (6)

Integral equations for elliptic problems with edge singularities and applications to the fourier-boundary element method ⋮ Dirichlet problems in polyhedral domains. II: Approximation by FEM and BEM ⋮ A posteriori error estimates for a nonconforming finite element discretization of the time-dependent Stokes problem, II: Analysis of the spatial estimator ⋮ Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³. Part II: Regularity in neighbourhoods of edges ⋮ Weighted regularization for composite materials in electromagnetism ⋮ Finite element method for elliptic problems with edge singularities

Cites Work

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• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Estimates in 𝐿_{𝑝} and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary
• Weighted spaces with nonhomogeneous norms and boundary value problems in domains with conical points
• Error estimates on the coeficients obtained by the singular function method
• Edge Behavior of the Solution of an Elliptic Problem
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron

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