Lower semicontinuous envelopes in $w^{1,1}\times l^p$

Ana Margarida Ribeiro; Elvira Zappale

Lower semicontinuous envelopes in $w^{1,1}\times l^p$

Analysis of PDEs 2012-11-13 v1

Authors: Ana Margarida Ribeiro , Elvira Zappale

Abstract

It is studied the lower semicontinuity of functionals of the type $\int_\Omega f(x,u,v, \nabla u)dx$ with respect to the $(W^{1,1}\times L^p)$ -weak \ast topology. Moreover in absence of lower semicontinuity, it is also provided an integral representation in $W^{1,1} \times L^p$ for the lower semicontinuous envelope.

Keywords

lower semicontinuity lower semicontinuous envelope integral representation weak star topology functionals W^{1,1} L^p

Cite

@article{arxiv.1211.2568,
  title  = {Lower semicontinuous envelopes in $w^{1,1}\times l^p$},
  author = {Ana Margarida Ribeiro and Elvira Zappale},
  journal= {arXiv preprint arXiv:1211.2568},
  year   = {2012}
}

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