The mixed problem for the Laplacian in Lipschitz domains
| Autor: | Ott, Katharine A., Brown, Russell M. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Potential analysis, 38 (2013), 1333-1364 (reference is for the original paper) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11118-012-9317-6 |
| Popis: | We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1. Comment: Version 5 includes a correction to one step of the main proof. Since the paper appeared long ago, this submission includes the complete paper, followed by a short section that gives the correction to one step in the proof |
| Databáze: | arXiv |
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