An approach to minimization under constraint: the added mass technique

TL;DR

This paper introduces a new minimization approach under constraints called the added mass technique, connecting it with established methods and applying it to constrained elliptic problems.

Contribution

It presents the added mass technique, linking it to Lions' Compactness by Concentration, and demonstrates its application to constrained semi-linear and quasi-linear elliptic equations.

Findings

The added mass technique effectively addresses constrained minimization problems.

Connections established between the new approach and Lions' method.

Applications show the technique's utility in elliptic PDEs.

Abstract

We present an approach to minimization under constraint. We explore the connections of this technique with the general method of Compactness by Concentration of P.L. Lions and present applications to some constrained semi-linear and quasi-linear elliptic problems.