Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces |
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Authors: | Svetlana Mayboroda Marius Mitrea |
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Institution: | 1. Department of Mathematics, University of Missouri at Columbia, Columbia, MO, 65211, USA
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Abstract: | We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain ${\Omega}$ , with boundary data in the Besov space ${B_{s}^{p,p} (\partial\Omega).}$ The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig 14], where the case p > 1 was treated. |
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