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Displaying similar documents to “Some problems of parabolic type with discontinuous nonlinearities on convex constraints”

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.

Parallelograms inscribed in a curve having a circle as π/2-isoptic

Andrzej Miernowski (2008)

Annales UMCS, Mathematica

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Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.