A relaxation result in BVxL^p for integral functionals depending on elastic strain and chemical composition

TL;DR

This paper establishes a relaxation result for a class of integral functionals involving elastic strain and chemical composition, relevant to thermochemical equilibria, image decomposition, and nonlinear elasticity.

Contribution

It provides a new integral representation for the relaxation of energy functionals depending on two vector fields with different behaviors.

Findings

Derived a relaxation formula for the energy functionals

Applicable to models in thermochemical equilibria and image processing

Enhanced understanding of variational problems involving multiple fields

Abstract

An integral representation result is obtained for the relaxation of a class of energy functionals depending on two vector fields with different behaviors which appear in the context of thermochemical equilibria and are related to image decomposition models and directors theory in nonlinear elasticity.