Optimal solvability for the Dirichlet and Neumann problem in dimension two
经典分析与常微分方程
2007-05-23 v1
摘要
We show existence and uniqueness for the solutions of the regularity and the Neumann problems for harmonic functions on Lipschitz domains with data in the Hardy spaces H^p, p>2/3, where This in turn implies that solutions to the Dirichlet problem with data in the Holder class C^{1/2}(\partial D) are themselves in C^{1/2}(D). Both of these results are sharp. In fact, we prove a more general statement regarding the H^p solvability for divergence form elliptic equations with bounded measurable coefficients. We also prove similar solvability result for the regularity and Dirichlet problem for the biharmonic equation on Lipschitz domains.
引用
@article{arxiv.math/0012254,
title = {Optimal solvability for the Dirichlet and Neumann problem in dimension two},
author = {Atanas Stefanov and Gregory Verchota},
journal= {arXiv preprint arXiv:math/0012254},
year = {2007}
}