Published Paper

Inserted: 27 jul 2023
Last Updated: 13 apr 2024

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

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 https://arxiv.org/abs/1606.01706, 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

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