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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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