# On the integral representation of variational functionals on $BD$

## TL;DR

This paper establishes an integral representation for a broad class of variational functionals defined on functions with Bounded Deformation, under mild continuity conditions, advancing the theoretical understanding of such functionals.

## Contribution

It provides a new integral representation result for variational functionals on BD spaces using the global relaxation method, with minimal continuity assumptions.

## Key findings

- Proves an integral representation for variational functionals on BD
- Uses the global relaxation method for the proof
- Requires mild continuity conditions on the functionals

## Abstract

Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions are required on the functionals.