L∞ a priori bounds for gradients of solutions to quasilinear inhomogeneous fast-growing parabolic systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Burczak, Jan¹ 

[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

关键词: Quasilinear parabolic systems;    p-Laplacian;    Regularity;    Boundedness of gradient;    Moser-type iteration;    Campanato's controllable growth;   

DOI  :  10.1016/j.jmaa.2012.04.020

来源: Elsevier

【 摘 要 】

We prove boundedness of gradients of solutions to quasilinear parabolic systems, the main part of which is a generalization to the p-Laplacian and its right-hand side's growth depending on the gradient is not slower (and generally strictly faster) than p - 1. This result may be seen as a generalization to the classical notion of a controllable growth of the right-hand side, introduced by Campanato, over gradients of p-Laplacian-like systems. Energy estimates and a nonlinear iteration procedure of the Moser type are Cornerstones of the used method. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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