Uniform estimates near the initial state for solutions to the two-phase parabolic problem

TL;DR

This paper proves optimal regularity near the initial state for solutions to the two-phase parabolic obstacle problem, accommodating initial data with $C^{1,1}$ regularity, using a general approach.

Contribution

It introduces a general method to establish optimal regularity near the initial state for two-phase parabolic problems with $C^{1,1}$ initial data.

Findings

Proves optimal regularity near the initial state.

Handles initial data in $C^{1,1}$ class.

Method applicable to a broad class of problems.

Abstract

This paper is devoted to a proof of optimal regularity, near the initial state, for weak solutions to the two-phase parabolic obstacle problem. The approach used here is general enough to allow us to consider the initial data belonging to the class $C^{1,1}$.