Continuity estimates for degenerate parabolic double-phase equations via nonlinear potentials

TL;DR

This paper investigates the regularity of solutions to degenerate parabolic double-phase equations, providing continuity estimates based on nonlinear potential theory, specifically elliptic Riesz potentials.

Contribution

It introduces new continuity estimates for solutions using nonlinear potentials, advancing understanding of degenerate double-phase equations.

Findings

Established continuity estimates for bounded weak solutions.

Connected solution regularity to elliptic Riesz potentials.

Enhanced theoretical framework for degenerate parabolic equations.

Abstract

In this article, we study regularity properties for degenerate parabolic double-phase equations. We establish continuity estimates for bounded weak solutions in terms of elliptic Riesz potentials on the right-hand side of the equation.