Weighted Sobolev spaces and regularity for polyhedral domains

DOI10.1016/j.cma.2006.10.022zbMath1173.35415arXivmath/0609101OpenAlexW1999509432MaRDI QIDQ1033381

Bernd Ammann, Victor Nistor

Publication date: 6 November 2009

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609101

zbMATH Keywords

weighted Sobolev spaceLaplace operatortrace theoremPoisson equationregularity of solutionswell posedness on polyhedral domains

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Sobolev spaces and \(\nabla\)-differential operators on manifolds. I: Basic properties and weighted spaces ⋮ HIGH-ORDER GALERKIN APPROXIMATIONS FOR PARAMETRIC SECOND-ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS ⋮ Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks ⋮ Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra II: Mesh Refinements and Interpolation ⋮ Regularity for eigenfunctions of Schrödinger operators ⋮ Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDES ⋮ Closure of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds and semi-Fredholm properties of differential operators on Lie manifolds ⋮ Bergman and Calderón projectors for Dirac operators ⋮ Function spaces on singular manifolds ⋮ A-priori analysis and the finite element method for a class of degenerate elliptic equations ⋮ Local mesh refinement for the discretization of Neumann boundary control problems on polyhedra ⋮ Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems ⋮ Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM ⋮ Optimal control under reduced regularity

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