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

  • Jihoon Ok,
  • Giovanni Scilla,
  • Bianca Stroffolini

摘要

We establish a partial regularity result for solutions of parabolic systems with general \(\varphi \) φ -growth, where \(\varphi \) 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 \(\varphi \) 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 \({\mathcal {A}}\) A -caloric approximation, which we prove without using the classical compactness method.