Displaying similar documents to “Evolution of subsets of 2 and parabolic problem for the Levi equation”

Levi equation and evolution of subsets of C 2

Zbigniew Slodkowski, Giuseppe Tomassini (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note we state some results obtained studying the evolution of compact subsets of C 2 by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.

Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations

Tuomo Kuusi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.