Young measures, Cartesian maps, and polyconvexity

Patrick Bernard (1) , Ugo Bessi (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di Matematica [Roma TRE]

We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map. The proof is based on Young measures.

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

Patrick Bernard, Ugo Bessi. Young measures, Cartesian maps, and polyconvexity. Journal of the Korean Mathematical Society, 2010, 47 (2), pp.331-350. ⟨10.4134/JKMS.2010.47.2.331⟩. ⟨hal-00294644v2⟩