Relaxation of certain integral functionals depending on strain and chemical composition
We provide a relaxation result in $BV \times L^q$, $1\leq q < +\infty$ as a first step towards the analysis of thermochemical equilibria.
Lower semicontinuous envelopes in $w^{1,1}\times l^p$
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.