Estimates of solutions for the parabolic $p$-Laplacian equation with measure via parabolic nonlinear potentials

TL;DR

This paper develops pointwise estimates for weak solutions to the parabolic p-Laplacian equation with measure data, using nonlinear parabolic potentials to analyze their behavior over time.

Contribution

It introduces a novel approach to estimate solutions of the parabolic p-Laplacian with measure data through nonlinear potentials, extending existing methods to the time-dependent setting.

Findings

Established pointwise bounds for solutions using nonlinear potentials.

Extended potential theory techniques to parabolic equations with measure data.

Provided new tools for analyzing regularity of solutions in measure-driven problems.

Abstract

For weak solutions to the evolutional $p$-Laplace equation with a time-dependent Radon measure on the right hand side we obtain pointwise estimates via a nonlinear parabolic potential.