Hölder-estimates for non-autonomous parabolic problems  with rough data

Hannes  Meinlschmidt; Joachim  Rehberg

doi:10.3934/eect.2016.5.147

Article Contents

2016, Volume 5, Issue 1: 147-184. Doi: 10.3934/eect.2016.5.147

This issue Previous Article The energy conservation for weak solutions to the relativistic Nordström-Vlasov system Next Article A matrix-valued generator $\mathcal{A}$ with strong boundary coupling: A critical subspace of $D((-\mathcal{A})^{\frac{1}{2}})$ and $D((-\mathcal{A}^*)^{\frac{1}{2}})$ and implications

Hölder-estimates for non-autonomous parabolic problems with rough data

Hannes Meinlschmidt^1, and
Joachim Rehberg^2,

1.
Technische Universität Darmstadt, Fachbereich Mathematik, Dolivostr. 15, D-64293 Darmstadt
2.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin

Received: February 28, 2015

Revised: January 31, 2016

Published: February 2016

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Abstract

In this paper we establish Hölder estimates for solutions to nonautonomous parabolic equations on non-smooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of Ladyshenskaya et al. [40], which also serves as the starting point for our investigations.

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Mathematics Subject Classification: 35B65, 35K10, 35K15.

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