Integral representation of unbounded variational functionals on Sobolev spaces
Résumé
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.
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