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

TL;DR

This paper investigates nonlinear parabolic PDEs with Orlicz growth, establishing existence, uniqueness, and regularity of solutions to the obstacle problem, including convergence and continuity properties.

Contribution

It introduces new existence and regularity results for obstacle problems involving parabolic equations with Orlicz-type growth conditions.

Findings

Existence and uniqueness of solutions to the obstacle problem.

Boundedness of weak solutions and convergence of supersolutions.

Continuity of solutions when the obstacle is continuous.

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.