Calculus of Variations and Geometric Measure Theory

D. Graziani

A new $L^1$ - lower semicontinuity result

created by graziani on 24 Oct 2005
modified on 13 Jan 2007


Accepted Paper

Inserted: 24 oct 2005
Last Updated: 13 jan 2007

Year: 2005


The aim of this work is to prove a chain rule and an $L^1$-lower semicontinuity theorems for integral functional defined on $BV(\Omega)$. Moreover we apply this result in order to obtain new relaxation and $\Gamma$-convergence result without any coerciveness and any continuity assumption of the integrand $f(x,s,p)$ with respect to the variable $s$.

Keywords: relaxation, Lower Semicontinuity, BV functions, Chain Rule