Boundedness and continuity of the time derivative in the parabolic Signorini problem

TL;DR

This paper proves that the time derivative in the parabolic Signorini problem is both bounded and Hölder continuous at regular free boundary points, advancing understanding of free boundary regularity.

Contribution

It establishes boundedness and Hölder continuity of the time derivative in the parabolic Signorini problem, a novel regularity result.

Findings

Time derivative is bounded in the parabolic Signorini problem.

Time derivative is Hölder continuous at regular free boundary points.

Enhances understanding of free boundary regularity in parabolic obstacle problems.

Abstract

We prove the boundedness of the time derivative in the parabolic Signorini problem, as well as establish its H\"older continuity at regular free boundary points.