Intrinsic Scalings with Non-standard Growth

TL;DR

This paper develops new regularity estimates for degenerate parabolic PDEs with Orlicz-type growth, using intrinsic scalings and geometric analysis, providing insights into solution smoothness even in stationary cases.

Contribution

It introduces a novel approach combining intrinsic scalings and geometric tangential analysis for Orlicz-type PDEs, advancing regularity theory.

Findings

Established interior Hölder regularity for solutions

Extended regularity results to time-stationary cases

Provided a framework for analyzing non-standard growth PDEs

Abstract

In this work, we investigate quantitative regularity estimates for degenerate parabolic partial differential equations, with a focus on Orlicz-type diffusive structures. Using a geometric tangential analysis tailored to these structures and a general notion of intrinsic scalings, we derive precise interior H\"older regularity estimates for bounded weak solutions. These results offer new insights, even in the time-stationary case.