Pointwise estimates for solutions of singular quasi-linear parabolic equations

TL;DR

This paper derives pointwise estimates for solutions to a class of singular quasi-linear parabolic equations with Radon measure data, using nonlinear Wolff potentials to understand solution behavior.

Contribution

It introduces a novel approach to estimate solutions of singular parabolic equations employing nonlinear Wolff potentials, extending previous methods to measure data.

Findings

Established pointwise bounds for solutions

Linked solution behavior to nonlinear Wolff potentials

Extended analysis to singular divergence-type equations

Abstract

For a class of singular divergence type quasi-linear parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via the nonlinear Wolff potentials.