On the relaxation of unbounded multiple integrals
Analysis of PDEs
2012-07-25 v2 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.1207.2652,
title = {On the relaxation of unbounded multiple integrals},
author = {Omar Anza Hafsa and Jean Philippe Mandallena},
journal= {arXiv preprint arXiv:1207.2652},
year = {2012}
}