Continuity of the temperature in a multi-phase transition problem

TL;DR

This paper proves local continuity of solutions to a complex multi-phase transition model, providing an explicit modulus of continuity and analyzing the impact of p-Laplacian diffusion.

Contribution

It establishes the local continuity of solutions to a doubly nonlinear parabolic equation modeling multi-phase transitions, including explicit regularity estimates and the effect of p-Laplacian diffusion.

Findings

Solutions are locally continuous.

An explicit modulus of continuity is derived.

The influence of p-Laplacian diffusion is analyzed.

Abstract

Locally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover, an explicit modulus of continuity is given. The effect of the $p$-Laplacian type diffusion is also considered.