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June 2009 Local Regularity Results for Second Order Elliptic Systems on Lipschitz Domains
Marius Mitrea, Michael Taylor
Funct. Approx. Comment. Math. 40(2): 175-184 (June 2009). DOI: 10.7169/facm/1246454027

Abstract

For a class of strongly elliptic, second order systems $L$ with rough coefficients on a Lipschitz domain $\Omega$, we show that if $Lu=0$ on $\Omega$ and $u$ vanishes on an open subset of the boundary, then weak a priori hypotheses on the nontangential maximal function of $u$ lead to strong estimates on $\nabla u$, in nontangential and Besov norms, near this subset.

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Marius Mitrea. Michael Taylor. "Local Regularity Results for Second Order Elliptic Systems on Lipschitz Domains." Funct. Approx. Comment. Math. 40 (2) 175 - 184, June 2009. https://doi.org/10.7169/facm/1246454027

Information

Published: June 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1181.35076
MathSciNet: MR2543555
Digital Object Identifier: 10.7169/facm/1246454027

Subjects:
Primary: 35B65, 35J55
Secondary: 31B25, 46E35

Rights: Copyright © 2009 Adam Mickiewicz University

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Vol.40 • No. 2 • June 2009
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