A convex dual variational formulation for non-convex optimization applied to a non-linear model of plates

TL;DR

This paper develops a dual variational framework for a non-linear plate model using convex analysis, providing new optimality conditions and establishing global existence results for related elasticity models.

Contribution

It introduces a convex dual variational formulation for a non-linear plate model, offering new optimality conditions and extending to global existence results.

Findings

Established a duality principle for the non-linear Kirchhoff-Love plate model

Derived new optimality conditions based on the dual formulation

Proved global existence results for a related elasticity model

Abstract

This article develops duality principles applicable to the non-linear Kirchhoff-Love model of plates. The results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. The main duality principle concerns a convex (in fact concave) dual variational formulation and related new optimality conditions for the model in question. Finally, in the last section we develop some global existence results for a similar model in elasticity.