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

초록

We establish a partial regularity result for solutions of parabolic systems with general phi$\phi$-growth, where phi$\phi$ 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 phi$\phi$-caloric approximation, which was introduced in Diening et al. (Calc Var Partial Differ Equ 56(4):27, 2017), and an improved version of the A$\mathcal{A}$-caloric approximation, which we prove without using the classical compactness method.

키워드