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.
New perturbation methods for nonlinear parabolic problems / T., Kuusi; Mingione, Giuseppe. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 98:4(2012), pp. 390-427. [10.1016/j.matpur.2012.02.004]
New perturbation methods for nonlinear parabolic problems
MINGIONE, Giuseppe
2012-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
