Young measures, Cartesian maps, and polyconvexity

TL;DR

This paper proves the existence of minimizers for a class of variational problems involving polyconvex integrands between manifolds, using Young measures for a straightforward approach.

Contribution

It provides a simple, direct proof of minimizer existence for polyconvex variational problems between manifolds utilizing Young measures.

Findings

Existence of minimizers established for polyconvex integrands.

Young measures effectively used in the proof.

Simplified proof approach compared to previous methods.

Abstract

We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map. The proof is based on Young measures.