3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization

TL;DR

This paper develops a 3D-2D dimension reduction technique for a nonlinear optimal design problem incorporating perimeter penalization, using $ extGamma$-convergence to derive an integral representation of the limit functional.

Contribution

It introduces a novel 3D-2D reduction approach for nonlinear optimal design problems with perimeter penalization within the $ extGamma$-convergence framework.

Findings

Derived an integral representation for the limit functional.

Established a rigorous dimension reduction result.

Provided a new approach for nonlinear optimal design problems.

Abstract

A 3D-2D dimension reduction for a nonlinear optimal design problem with a perimeter penalization is performed in the realm of $\Gamma$-convergence, providing an integral representation for the limit functional.