Approximation and relaxation of perimeter in the Wiener space

Michael Goldman (1) , Matteo Novaga (2)

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

We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L^2-topology. We also show that the rescaled Allen-Cahn functionals approximate this relaxed functional in the sense of Gamma-convergence.

Mots clés: Gamma convergence; relaxation; Wiener space; isoperimetry; Modica-Mortola; sets of finite perimeter

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Michael Goldman, Matteo Novaga. Approximation and relaxation of perimeter in the Wiener space. Annales de l'Institut Henri Poincaré, 2012. ⟨hal-00609031⟩