Symmetry in variational principles and applications

TL;DR

This paper develops symmetric versions of classical variational principles, enabling the detection of special critical sequences with symmetry properties, and applies these to PDEs, fixed point theory, and geometric analysis.

Contribution

It introduces symmetric formulations of variational principles within non-smooth critical point theory, enhancing the analysis of symmetric solutions in various mathematical fields.

Findings

Detection of Palais-Smale sequences with symmetry

Applications to PDEs and fixed point problems

Enhanced understanding of symmetric solutions in geometric analysis

Abstract

We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications to PDEs, fixed point theory and geometric analysis.