Lipschitz Domains, Domains with Corners, and the Hodge Laplacian

DOI10.1080/03605300500299547zbMath1082.31007arXivmath/0408438OpenAlexW1976170795MaRDI QIDQ5713467

András Vasy, Marius Mitrea, Michael E. Taylor

Publication date: 14 December 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408438

zbMATH Keywords

regularityconvexityRiemannian manifoldsLipschitz domainsHodge Laplacianmanifolds with corners

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Boundary value problems on manifolds (58J32) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (9)

Spectral theory for perturbed Krein Laplacians in nonsmooth domains ⋮ Elliptic boundary problems on manifolds with polycylindrical ends ⋮ Elliptic differential operators on Lipschitz domains and abstract boundary value problems ⋮ Boundary value problems for the Laplacian in convex and semiconvex domains ⋮ The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates ⋮ A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains ⋮ DIFFRACTION BY EDGES ⋮ Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition ⋮ On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds

Cites Work

• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Boundary layer methods for Lipschitz domains in Riemannian manifolds
• Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem
• Finite energy solutions of Maxwell's equations and constructive Hodge decompositions on nonsmooth Riemannian manifolds
• Sharp Hodge decompositions, Maxwell's equations, and vector Poisson problems on nonsmooth, three-dimensional Riemannian manifolds
• Singularities of electromagnetic fields in polyhedral domains
• Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds
• Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domains
• Differential forms on riemannian manifolds
• Cauchy integrals on Lipschitz curves and related operators
• Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien
• The Harmonic Operator for Exterior Differential Forms
• Generalized Dirac operators on nonsmooth manifolds and Maxwell's equations

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