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

Mitrea, Marius

doi:10.1090/S0002-9939-02-06551-6

A note on Besov regularity of layer potentials and solutions of elliptic PDE’s
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Proc. Amer. Math. Soc. 130 (2002), 2599-2607 Request permission

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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