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

Casimir Lindfors

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

Analysis of PDEs 2016-04-12 v1

Authors: Casimir Lindfors

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.

Keywords

obstacle problem parabolic equations generalized p-laplacian orlicz-type growth weak solutions weak supersolutions existence of solution

Cite

@article{arxiv.1604.02897,
  title  = {Obstacle problem for a class of parabolic equations of generalized $p$-Laplacian type},
  author = {Casimir Lindfors},
  journal= {arXiv preprint arXiv:1604.02897},
  year   = {2016}
}

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