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

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• 作者：Patrick Winkert^a ; ^{winkert@math.tu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; Rico Zacher^b
• 关键词：35K59 ; 35K92
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：145
• 期：Complete
• 页码：1-23
• 全文大小：767 K

文摘

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)$p(t,x)$-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.