Integral representation and relaxation of local functionals on Cheeger-Sobolev spaces

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

1 MIPA - Mathématiques, Informatique, Physique, et Applications / Université de Nîmes

We prove an integral representation theorem for local functionals with polynomial growth defined on Cheeger-Sobolev spaces. More precisely, we give a version of the well-known Buttazzo-Dal maso integral representation theorem in the framework of Cheeger-Sobolev spaces. The integral representation theorem is used to prove a relaxation theorem.

Domaines: Mathématiques [math]; Analyse classique [math.CA]

Omar Anza Hafsa, Jean-Philippe Mandallena. Integral representation and relaxation of local functionals on Cheeger-Sobolev spaces. Nonlinear Analysis: Theory, Methods and Applications, 2022, 217, ⟨10.1016/j.na.2021.112744⟩. ⟨hal-03270938v2⟩