On the relaxation of unbounded multiple integrals

Omar Anza Hafsa (1) , Jean Philippe Mandallena (2)

1 M3 - Modélisation Mathématique en Mécanique
2 MIPA - Mathématiques, Informatique, Physique, et Applications / Université de Nîmes

We study the relaxation of multiple integrals of the calculus of variations, where the integrands are nonconvex with convex effective domain and can take the value \infty. We use local techniques based on measure arguments to prove integral representation in Sobolev spaces of functions which are almost everywhere differentiable. Applications are given in the scalar case and in the case of integrands with quasiconvex growth and p(x)-growth.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Omar Anza Hafsa, Jean Philippe Mandallena. On the relaxation of unbounded multiple integrals. 2012. ⟨hal-00958314⟩