Critical points of a perturbed Otha-Kawasaki functional

TL;DR

This paper studies a perturbed version of the Otha-Kawasaki functional and constructs multiple critical points near translated Schwarz P surfaces with fixed volume, advancing understanding of pattern formation in phase separation models.

Contribution

It introduces a novel perturbation approach to find multiple critical points near known minimal surfaces in the Otha-Kawasaki functional.

Findings

Existence of at least four critical points close to Schwarz P surface translations

Construction of critical points with fixed volume

Extension of variational methods to perturbed functionals

Abstract

In the paper, we consider a small perturbation of the Otha-Kawasaki functional and we construct at least four critical points close to suitable translations of the Schwarz P surface with fixed volume.