Calculus of Variations and Geometric Measure Theory
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R. Cristoferi - G. Gravina

On the relaxation of functionals with contact terms on non-smooth domains

created by gravina on 20 Oct 2020



Inserted: 20 oct 2020

Year: 2020

ArXiv: 2010.03212 PDF


We provide the integral representation formula for the relaxation in $BV(\Omega; \mathbb{R}^M)$ with respect to strong convergence in $L^1(\Omega; \mathbb{R}^M)$ of a functional with a boundary contact energy term. This characterization is valid for a large class of surface energy densities, and for domains satisfying mild regularity assumptions. Motivated by some classical examples where lower semicontinuity fails, we analyze the extent to which the geometry of the set enters the relaxation procedure.

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