The Lp regularity problem on lipschitz domains

Joel Kilty; Zhongwei Shen

doi:10.1090/S0002-9947-2010-05076-7

The L^p regularity problem on lipschitz domains

Joel Kilty
, Zhongwei Shen

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

This paper contains two results on the L^p regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the L^p regularity problem is equivalent to that of the L^p′ 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 Hölder condition with exponent p.

Original language	English
Pages (from-to)	1241-1264
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	363
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9947-2010-05076-7
State	Published - Mar 2011

Keywords

Dirichlet problem
Lipschitz domains
Regularity problem

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-2010-05076-7

Cite this

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title = "The Lp regularity problem on lipschitz domains",

abstract = "This paper contains two results on the Lp regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the Lp regularity problem is equivalent to that of the Lp′ Dirichlet problem. For higher order elliptic equations and systems, we show that if p > 2, the solvability of the Lp regularity problem is equivalent to a weak reverse H{\"o}lder condition with exponent p.",

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AB - This paper contains two results on the Lp regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the Lp regularity problem is equivalent to that of the Lp′ Dirichlet problem. For higher order elliptic equations and systems, we show that if p > 2, the solvability of the Lp regularity problem is equivalent to a weak reverse Hölder condition with exponent p.

KW - Dirichlet problem

KW - Lipschitz domains

KW - Regularity problem

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