Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space

TL;DR

This paper investigates the combined effects of homogenization and dimension reduction on energy functionals defined on manifold-valued BV spaces, using Gamma-convergence to derive integral representations.

Contribution

It introduces a novel approach to analyze manifold-valued BV functions under homogenization and dimension reduction via Gamma-convergence, extending existing theories.

Findings

Derived integral representation for the homogenized and dimension-reduced energy functional.

Established Gamma-convergence results for manifold-valued Sobolev functions with linear growth.

Provided a framework for analyzing manifold-constrained variational problems in reduced dimensions.

Abstract

We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $\Gamma$-convergence, providing an integral representation result in the space of manifold constrained functions with bounded variation