Integral representation of unbounded variational functionals on Sobolev spaces

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

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

In this paper we establish an unbounded version of the integral representation theorem by Buttazzo and Dal Maso (see [BDM85] and also [BFLM02]). More precisely, we prove an integral representation theorem (with a formula for the integrand) for functionals defined on $W^{1,p}$ with $p>N$ ($N$ being the dimension) that do not satisfy a standard $p$-growth condition from above and can take infinite values. Applications to $\Gamma$-convergence, relaxation and homogenization are also developed.

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

Omar Anza Hafsa, Jean-Philippe Mandallena. Integral representation of unbounded variational functionals on Sobolev spaces. Ricerche di matematica, inPress, ⟨10.1007/s11587-021-00652-7⟩. ⟨hal-03270923⟩