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arXiv · 1604.02897

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

Casimir Lindfors
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Abstract

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.

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Casimir Lindfors. 2016-04-11. Obstacle problem for a class of parabolic equations of generalized $p$-Laplacian type. https://arxiv.org/abs/1604.02897

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