Evolution Equations and Control Theory (EECT)

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

Pages: 147 - 184, Volume 5, Issue 1, March 2016      doi:10.3934/eect.2016.5.147

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Hannes Meinlschmidt - Technische Universität Darmstadt, Fachbereich Mathematik, Dolivostr. 15, D-64293 Darmstadt, Germany (email)
Joachim Rehberg - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany (email)

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.

Keywords:  Linear, second order parabolic equations, non-smooth data, Hölder continuity of the solution.
Mathematics Subject Classification:  35B65, 35K10, 35K15.

Received: March 2015;      Revised: February 2016;      Available Online: March 2016.