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Abstract evolution equations on variable domains : an approach by minimizing movements

Ugo Gianazza; Giuseppe Savaré — 1996

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Boundary estimates for certain degenerate and singular parabolic equations

Benny Avelin; Ugo Gianazza; Sandro Salsa — 2016

Journal of the European Mathematical Society

We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic $p$ -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part $S_{T}$ of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular...

Evolution Problems and Minimizing Movements

Ugo Gianazza; Massimo Gobbino; Giuseppe Savarè — 1994

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

We recall the definition of Minimizing Movements, suggested by E. De Giorgi, and we consider some applications to evolution problems. With regards to ordinary differential equations, we prove in particular a generalization of maximal slope curves theory to arbitrary metric spaces. On the other hand we present a unifying framework in which some recent conjectures about partial differential equations can be treated and solved. At the end we consider some open problems.

Harnack's estimates: positivity and local behavior of degenerate and singular parabolic equations.

DiBenedetto, Emmanuele; Gianazza, Ugo; Safonov, Mikhail; Urbano, José Miguel; Vespri, Vincenzo — 2007

Boundary Value Problems [electronic only]

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