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 et al. (Calc Var Partial Differ Equ 56(4):27, 2017), and an improved version of the A-caloric approximation, which we prove without using the classical compactness method.
Partial regularity for degenerate parabolic systems with general growth via caloric approximations / Ok, Jihoon; Scilla, Giovanni; Stroffolini, Bianca. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 63:4(2024). [10.1007/s00526-024-02687-8]
Partial regularity for degenerate parabolic systems with general growth via caloric approximations
Scilla, Giovanni;Stroffolini, Bianca
2024
Abstract
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 et al. (Calc Var Partial Differ Equ 56(4):27, 2017), and an improved version of the A-caloric approximation, which we prove without using the classical compactness method.File | Dimensione | Formato | |
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