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Zbl 0589.31005
Verchota, Gregory
Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains.
(English)
[J] J. Funct. Anal. 59, 572-611 (1984). ISSN 0022-1236

The author considers the classical layer potentials for harmonic functions on the boundary $\partial G$ of a bounded Lipschitz domain G in ${\bbfR}\sp n$ for use in Dirichlet and Neumann problems. It is shown that these potentials are invertible operators on $L\sp 2(\partial G)$ and some subspaces. In the case $n=2$ the layer potentials are shown to be invertible on every $L\sp p(\partial G)$, $1<p<\infty$.
[G.Dziuk]
MSC 2000:
*31B25 Boundary behavior of harmonic functions (higher-dim.)
35J05 Laplace equation, etc.
47B10 Operators defined by summability properties

Keywords: Lipschitz boundary; regularity; layer potentials; harmonic functions; Dirichlet and Neumann problems

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