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

Jihoon Ok, Giovanni Scilla,Bianca Stroffolini

arxiv(2023)

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摘要
We establish a partial regularity result for solutions of parabolic systems with general φ-growth, where φ 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 φ-caloric approximation, which was introduced in Diening, Schwarzacher, Stroffolini and Verde (2017) (arXiv:1606.01706), and an improved version of the 𝒜-caloric approximation, which we prove without using the classical compactness method.
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