New perturbation methods for nonlinear parabolic problems

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Abstract

We develop methods aimed at deriving regularity results for solutions to nonlinear degenerate parabolic equations and systems via local perturbation; as a consequence we obtain, in a unified way, Lipschitz continuity of solutions under weak parabolicity assumptions, and gradient continuity results in borderline cases. Nonlinear Schauder estimates as those of Misawa (2002) [29] are recovered and extended to more general settings. © 2012 Elsevier Masson SAS.

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APA

Kuusi, T., & Mingione, G. (2012). New perturbation methods for nonlinear parabolic problems. Journal Des Mathematiques Pures et Appliquees, 98(4), 390–427. https://doi.org/10.1016/j.matpur.2012.02.004

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