Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains (Q1073972)

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 \(L^ p(\partial G)\), \(1<p<\infty\).