The $L^p$ Regularity Problem on Lipschitz Domains

Joel Kilty; Zhongwei Shen

The $L^p$ Regularity Problem on Lipschitz Domains

Analysis of PDEs 2009-05-01 v2

Authors: Joel Kilty , Zhongwei Shen

Abstract

This paper contains two results on the $L^p$ regularity problem on Lipschitz domains. For second order elliptic systems and $1<p<\infty$ , we prove that the solvability of the $L^p$ regularity problem is equivalent to that of the $L^{p^\prime}$ Dirichlet problem. For higher order elliptic equations and systems, we show that if $p>2$ , the solvability of the $L^p$ regularity problem is equivalent to a weak reverse H\"older condition with exponent $p$ .

Keywords

regularity for elliptic equations lp spaces and inequalities dirichlet problem

Cite

@article{arxiv.0904.3906,
  title  = {The $L^p$ Regularity Problem on Lipschitz Domains},
  author = {Joel Kilty and Zhongwei Shen},
  journal= {arXiv preprint arXiv:0904.3906},
  year   = {2009}
}

Comments

To appear in Trans. of AMS. Updated to fix formatting issues

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