Relaxation et passage 3D-2D avec contraintes de type d\'eterminant

TL;DR

This paper develops tools and methods for relaxation and 3D-2D passage in the context of determinant constraints, providing a comprehensive Gamma-convergence proof for the positive determinant case.

Contribution

It introduces a complete set of tools for handling relaxation and 3D-2D passage with determinant constraints and offers a rigorous Gamma-convergence proof under positive determinant conditions.

Findings

Established a Gamma-convergence framework for determinant constraints.

Provided a complete proof for 3D-2D passage with positive determinant.

Developed new methods for relaxation under determinant constraints.

Abstract

The goal of this paper is, on the one hand, to make available a set of tools and methods to deal with relaxation and 3D-2D passage with determinant type constraints, and, on the other hand, to give a complete proof of the 3D-2D passage by Gamma-convergence under the constraint determinant positive.