Partial regularity for degenerate parabolic systems with general growth via caloric approximations

TL;DR

This paper proves partial regularity for solutions to degenerate parabolic systems with general growth conditions using novel caloric approximation techniques, advancing understanding of regularity in complex nonlinear systems.

Contribution

It introduces a unified approach for partial regularity that is independent of degeneracy, utilizing new caloric approximation results without classical compactness methods.

Findings

Established partial regularity for systems with Orlicz growth

Developed a new aloric approximation method

Proved regularity results without classical compactness

Abstract

We establish a partial regularity result for solutions of parabolic systems with general $\varphi$-growth, where $\varphi$ is an Orlicz function. In this setting we can develop a unified approach that is independent of the degeneracy of system and relies on two caloric approximation results: the $\varphi$-caloric approximation, which was introduced in Diening, Schwarzacher, Stroffolini and Verde (2017) (arXiv:1606.01706), and an improved version of the \mathcal{A}-caloric approximation, which we prove without using the classical compactness method.