Obstacle problem for a class of parabolic equations of generalized p-Laplacian type

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• 作者：Casimir Lindfors ^{casimir.lindfors@aalto.fi" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Degenerate/singular parabolic equations ; General growth conditions ; Obstacle problem
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：261
• 期：10
• 页码：5499-5540
• 全文大小：478 K

文摘

We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and that a uniformly bounded sequence of weak supersolutions converges to a weak supersolution. Moreover, we prove that if the obstacle is continuous, so is the solution.