The mixed problem in L^p for some two-dimensional Lipschitz domains
偏微分方程分析
2010-07-27 v1
摘要
We consider the mixed problem for the Laplace operator in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. The boundary of the domain is decomposed into two disjoint sets D and N. We suppose the Dirichlet data, f_D has one derivative in L^p(D) of the boundary and the Neumann data is in L^p(N). We find conditions on the domain and the sets D and N so that there is a p_0>1 so that for p in the interval (1,p_0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L^p.
引用
@article{arxiv.math/0505461,
title = {The mixed problem in L^p for some two-dimensional Lipschitz domains},
author = {Loredana Lanzani and Luca Capogna and Russell Brown},
journal= {arXiv preprint arXiv:math/0505461},
year = {2010}
}