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arXiv · 2307.14779

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

Jihoon Ok·Giovanni Scilla·Bianca Stroffolini
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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.

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Jihoon Ok, Giovanni Scilla, Bianca Stroffolini. 2023-07-27. Partial regularity for degenerate parabolic systems with general growth via caloric approximations. https://doi.org/10.1007/s00526-024-02687-8

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