Calculus of Variations and Geometric Measure Theory
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T. Kuusi - G. Mingione

New perturbation methods for nonlinear parabolic systems

created by mingione on 29 Sep 2012


Inserted: 29 sep 2012
Last Updated: 29 sep 2012

Journal: J. Math. Pures et Appl. (Ser. IX)
Volume: 98
Pages: 390-427
Year: 2012


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 \cite{misa1} are recovered and extended to more general settings.


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