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A note on Besov regularity of layer potentials and solutions of elliptic PDE's

Author: Marius Mitrea
Journal: Proc. Amer. Math. Soc. 130 (2002), 2599-2607
MSC (2000): Primary 35B65, 31B10; Secondary 42B20, 46E35
Published electronically: April 17, 2002
MathSciNet review: 1900867
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Abstract: Let $L$ be a second order, (variable coefficient) elliptic differential operator and let $u\in B^{p,p}_\alpha(\Omega)$, $1<p<\infty$, $\alpha>0$, satisfy $Lu=0$ in the Lipschitz domain $\Omega$. We show that $u$ can exhibit more regularity on Besov scales for which smoothness is measured in $L^\tau$ with $\tau<p$. Similar results are valid for functions representable in terms of layer potentials.

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Additional Information

Marius Mitrea
Affiliation: Department of Mathematics, University of Missouri at Columbia, Columbia, Missouri 65211

Keywords: Besov space regularity, Lipschitz domains, layer potentials, smoothness, elliptic PDE
Received by editor(s): March 16, 2001
Published electronically: April 17, 2002
Additional Notes: The author was partially supported by NSF grant DMS-9870018
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society

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