Displaying similar documents to “Curves of maximal slope and parabolic variational inequalities on non-convex constraints”

Some problems of parabolic type with discontinuous nonlinearities on convex constraints

Marlène Frigon, Antonio Marino, Claudio Saccon (1990)

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

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We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.

Plane maximal curves

Angela Aguglia, Gábor Korchmáros, Fernando Torres (2001)

Acta Arithmetica

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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

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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.