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

Riccardo Cristoferi; Giovanni Gravina

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arXiv · 2010.03212

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

Riccardo Cristoferi·Giovanni Gravina

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Abstract

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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Riccardo Cristoferi, Giovanni Gravina. 2020-10-07. On the relaxation of functionals with contact terms on non-smooth domains. https://arxiv.org/abs/2010.03212

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