Irregular Time Dependent Obstacles

TL;DR

This paper investigates the obstacle problem for the Evolutionary p-Laplace Equation with irregular, discontinuous obstacles in time, demonstrating that two different methods produce the same solution.

Contribution

It introduces two distinct procedures for solving the obstacle problem with irregular obstacles and proves their equivalence.

Findings

Both procedures yield the same solution.

The methods handle obstacles without regularity in time.

The work extends understanding of obstacle problems with irregular data.

Abstract

We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.