$L^\infty$-estimates for parabolic systems with VMO-coefficients

Horst Heck; Matthias Hieber; Kyriakos Stavrakidis

doi:10.3934/dcdss.2010.3.299

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2010, Volume 3, Issue 2: 299-309. Doi: 10.3934/dcdss.2010.3.299

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$L^\infty$-estimates for parabolic systems with VMO-coefficients

1.
Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt

Received: June 2009

Published: June 2010

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Abstract

In this paper we prove $L^\infty$-a priori estimates for parabolic evolution equations in non-divergence form on all of $\R^n$ for bounded coefficients having only vanishing mean oscillation, thus allowing in particular non continuous coefficients.

Keywords:

Parabolic systems,
VMO,
$L^\infty$.

Mathematics Subject Classification: 35J45, 35K55.

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