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arXiv · 1512.04328

Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth

Patrick Winkert·Rico Zacher
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Abstract

In this paper we study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds for weak solutions of such problems. Our results seem to be new even in the constant exponent case.

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Patrick Winkert, Rico Zacher. 2015-12-14. Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth. https://arxiv.org/abs/1512.04328

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