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

Author(s): Marius Mitrea
Journal: Proc. Amer. Math. Soc. 130 (2002), 2599-2607.
MSC (2000): Primary 35B65, 31B10; Secondary 42B20, 46E35
Posted: April 17, 2002
MathSciNet review: 1900867
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Abstract: Let be a second order, (variable coefficient) elliptic differential operator and let $u\in B^{p,p}_\alpha(\Omega)$ , $1<p<\infty$ , $\alpha>0$ , satisfy in the Lipschitz domain $\Omega$ . We show that 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
Email: marius@math.missouri.edu

DOI: 10.1090/S0002-9939-02-06551-6
PII: S 0002-9939(02)06551-6
Keywords: Besov space regularity, Lipschitz domains, layer potentials, smoothness, elliptic PDE
Received by editor(s): March 16, 2001
Posted: April 17, 2002
Additional Notes: The author was partially supported by NSF grant DMS-9870018
Communicated by: Andreas Seeger
Copyright of article: Copyright 2002, American Mathematical Society

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