Displaying similar documents to “A refined Brunn-Minkowski inequality for convex sets”

Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set

Luciano Carbone, Doina Cioranescu, Riccardo De Arcangelis, Antonio Gaudiello (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness...

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...