Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coeffcients from Kato-type classes

TL;DR

This paper establishes local boundedness, continuity, and an intrinsic Harnack inequality for solutions to a broad class of quasi-linear degenerate parabolic equations with coefficients from Kato-type classes, advancing understanding of their regularity.

Contribution

It introduces new regularity results for solutions to degenerate parabolic equations with Kato-class coefficients, including Harnack inequality and continuity properties.

Findings

Solutions are locally bounded and continuous.

Positive solutions satisfy an intrinsic Harnack inequality.

The results apply to equations with measurable coefficients from Kato-type classes.

Abstract

For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coeffcients and lower order terms from non-linear Kato-type classes, we prove local boundedness and continuity of solutions, and the intrinsic Harnack inequality for positive solutions.