Counterexamples to the well-posedness of 𝐿^{𝑝} transmission boundary value problems for the Laplacian

DOI10.1090/S0002-9939-07-08686-8zbMath1381.35250WikidataQ125026012 ScholiaQ125026012MaRDI QIDQ3432760

Irina Mitrea, Katharine A. Ott

Publication date: 18 April 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

spectrumsectortransmission boundary value problem

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) General theory of partial differential operators (47F05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35)

Related Items

Singular Integral Operators on C 1 Manifolds and C 1 Curvilinear Polygons ⋮ The mixed problem for the Lamé system in a class of Lipschitz domains

Cites Work

• Unnamed Item
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Transmission problems and spectral theory for singular integral operators on Lipschitz domains
• Layer potentials and Hodge decompositions in two dimensional Lipschitz domains.