Displaying similar documents to “Compensated convexity and its applications”

On the points of non-differentiability of convex functions

David Pavlica (2004)

Commentationes Mathematicae Universitatis Carolinae

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We characterize sets of non-differentiability points of convex functions on ℝ n . This completes (in ℝ n ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.

On the unique extension problem for functionals of the calculus of variations

Luciano Carbone, Riccardo De Arcangelis (2001)

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

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By drawing inspiration from the treatment of the non parametric area problem, an abstract functional is considered, defined for every open set in a given class of open subsets of R n and every function in C ∞ ⁢ R n , and verifying suitable assumptions of measure theoretic type, of invariance, convexity, and lower semicontinuity. The problem is discussed of the possibility of extending it, and of the uniqueness of such extension, to a functional verifying analogous properties, but defined in wider...