A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials

DOI10.1090/S0002-9947-08-04384-5zbMath1148.35020MaRDI QIDQ3508038

Dorina Mitrea

Publication date: 27 June 2008

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

zbMATH Keywords

Dirichlet problemSobolev spacesNeumann problemPoisson problemLipschitz domainGreen potentials

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Integral representations, integral operators, integral equations methods in two dimensions (31A10)

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Cites Work

• Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
• A local version of real Hardy spaces
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• Clifford wavelets, singular integrals, and Hardy spaces
• Integrability of Green potentials in fractal domains
• Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
• Sharp estimates for Green potentials on non-smooth domains
• The inhomogeneous Dirichlet problem in Lipschitz domains
• The Neumann problem on Lipschitz domains in Hardy spaces of order less than one
• $L^q$-estimates for Green potentials in Lipschitz domains.
• On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
• Interpolation Between H p Spaces: The Real Method
• Layer potentials and Hodge decompositions in two dimensional Lipschitz domains.
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