Layer potentials and Hodge decompositions in two dimensional Lipschitz domains.

DOI10.1007/s002080100266zbMath1098.42500OpenAlexW2083899393MaRDI QIDQ5957318

Dorina Mitrea

Publication date: 7 November 2002

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

Full work available at URL: https://doi.org/10.1007/s002080100266

zbMATH Keywords

Hodge decompositionlayer potentialLipschitz domain

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in two dimensions (31A10)

Related Items (10)

Transmission problems and spectral theory for singular integral operators on Lipschitz domains ⋮ Dirichlet and Neumann problems for elliptic equations with singular drifts on Lipschitz domains ⋮ A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials ⋮ Lp Neumann problem for some Schrödinger equations in (semi-)convex domains ⋮ On the Besov regularity of conformal maps and layer potentials on nonsmooth domains. ⋮ The mixed problem for the Laplacian in Lipschitz domains ⋮ Several non-standard problems for the stationary Stokes system ⋮ Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions ⋮ The mixed problem in Lipschitz domains with general decompositions of the boundary ⋮ Counterexamples to the well-posedness of 𝐿^{𝑝} transmission boundary value problems for the Laplacian

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