Calculus of Variations and Geometric Measure Theory

J. Ok - G. Scilla - B. Stroffolini

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

created by scilla on 27 Jul 2023
modified on 17 May 2024


Published Paper

Inserted: 27 jul 2023
Last Updated: 17 may 2024

Journal: Calculus of Variations and Partial Differential Equations
Volume: 63
Number: 105
Year: 2024
Doi: 10.1007/s00526-024-02687-8

ArXiv: 2307.14779 PDF


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, and an improved version of the $\mathcal A$-caloric approximation, which we prove without using the classical compactness method.

Keywords: Partial regularity, degenerate parabolic systems, caloric approximation, Orlicz growth