On the Time Derivative in an Obstacle Problem

TL;DR

This paper proves that the time derivative of solutions to the obstacle problem for the Evolutionary p-Laplace Equation exists in Sobolev's sense when the obstacle is sufficiently smooth, for p > 2.

Contribution

It establishes the existence of the time derivative in Sobolev's sense for obstacle problems related to the Evolutionary p-Laplace Equation with smooth obstacles.

Findings

Time derivative exists in Sobolev's sense under smooth obstacle conditions

Results apply for p > 2 in the Evolutionary p-Laplace Equation

Advances understanding of regularity in obstacle problems

Abstract

I prove that the time derivative for the solution of the obstacle problem related to the Evolutionary p-Laplace Equation exists in Sobolev's sense, provided that the given obstacle is smooth enough. We keep p > 2.