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Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains. (English) Zbl 0589.31005
The author considers the classical layer potentials for harmonic functions on the boundary \(\partial G\) of a bounded Lipschitz domain G in \({\mathbb{R}}^ n\) for use in Dirichlet and Neumann problems. It is shown that these potentials are invertible operators on \(L^ 2(\partial G)\) and some subspaces. In the case \(n=2\) the layer potentials are shown to be invertible on every \(L^ p(\partial G)\), \(1<p<\infty\).
Reviewer: G.Dziuk

MSC:
31B25 Boundary behavior of harmonic functions in higher dimensions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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