H^s versus C^0-weighted minimizers

TL;DR

This paper investigates semi-linear problems with the fractional Laplacian, showing that local minimizers in a weighted C^0-topology are also local minimizers in the natural H^s-topology, under subcritical or critical growth conditions.

Contribution

It establishes the equivalence of local minimizers in weighted C^0-topology and H^s-topology for fractional Laplacian problems, extending understanding of minimizer stability.

Findings

Weighted C^0-local minimizers are H^s-local minimizers

Results apply under subcritical and critical growth conditions

Enhances the theoretical framework for fractional Laplacian variational problems

Abstract

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.