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

Abstract

We establish a partial regularity result for solutions of parabolic systems with general $\ddot{I}†$-growth, where $\ddot{I}†$ 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 $\ddot{I}†$-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.