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

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June 2010, 3(2): 299-309. doi: 10.3934/dcdss.2010.3.299

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

Horst Heck ^1, , Matthias Hieber ^1, and Kyriakos Stavrakidis ^1,

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

Received June 2009 Published April 2010

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

Mathematics Subject Classification: 35J45, 35K5.

Citation: Horst Heck, Matthias Hieber, Kyriakos Stavrakidis. $L^\infty$-estimates for parabolic systems with VMO-coefficients. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 299-309. doi: 10.3934/dcdss.2010.3.299

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