The $L^p$ Regularity Problem on Lipschitz Domains

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dc.creatorKilty, Joel
dc.creatorShen, Zhongwei
dc.date2009-04-24
dc.date2009-04-30
dc.date.accessioned2026-07-07T13:09:50Z
dc.date.available2026-07-07T13:09:50Z
dc.descriptionThis 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 Hölder condition with exponent $p$.
dc.descriptionTo appear in Trans. of AMS. Updated to fix formatting issues
dc.identifierhttps://arxiv.org/abs/0904.3906
dc.identifierhttp://arxiv.org/abs/0904.3906
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228873
dc.subjectAnalysis of PDEs
dc.subject35J55; 35J40
dc.titleThe $L^p$ Regularity Problem on Lipschitz Domains
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