Lower semicontinuous envelopes in $W^{1,1}\times L^{p}$
Volume 101 / 2014
Banach Center Publications 101 (2014), 187-206
MSC: 49J45; 74F99.
DOI: 10.4064/bc101-0-15
Abstract
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 is studied. Moreover, in absence of lower semicontinuity, an integral representation in $W^{1,1}\times L^p$ for the lower semicontinuous envelope is also provided.
