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

2016/04/11 by Casimir Lindfors, Lindfors, Casimir
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1604.02897

arxiv created 2016/04/11 · openalex publication_date 2016/04/11 · arxiv updated 2016/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Stability of solutions to obstacle problems with generalized Orlicz growth
• Optimal regularity for the obstacle problem for the p-Laplacian
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• The Obstacle Problem for Quasilinear Stochastic PDEs with non-homogeneous operator