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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

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 and Continuous Dynamical Systems - S, 2010, 3 (2) : 299-309. doi: 10.3934/dcdss.2010.3.299
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