Representation, relaxation and convexity for variational problems in Wiener spaces

Antonin Chambolle (1) , Michael Goldman (1) , Matteo Novaga (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Dipartimento di Matematica Pura e Applicata [Padova]

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.

Mots clés: convexity; semi-continuity; representations formulas; BV; Wiener spaces

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Probabilités [math.PR]

Antonin Chambolle, Michael Goldman, Matteo Novaga. Representation, relaxation and convexity for variational problems in Wiener spaces. Journal de Mathématiques Pures et Appliquées, 2013. ⟨hal-00627083v4⟩