Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

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Abstract

We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.
Original languageEnglish
Pages (from-to)4268 - 4283
Number of pages16
JournalJournal of Differential Equations
Volume246
Issue number11
DOIs
Publication statusPublished - 2009
Externally publishedYes

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