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Nonlinear Partial Differential EquationsAdvanced Harmonic Analysis ResearchGeometric Analysis and Curvature Flows

The Concentration-Compactness Principle for the Fractional Laplacian on Lattice Graphs

Lidan Wang, Yanhua Zhao

2026.6.22Bulletin of the Malaysian Mathematical Sciences Society

DOI: 10.1007/s40840-026-02134-1

Abstract

In this paper, we prove the fractional discrete Sobolev inequality and concentration-compactness principle at infinity for the fractional Laplacian on lattice graphs $$\mathbb {Z}^d$$ . As an application, we show the existence of extremal function for a supercritical fractional discrete Sobolev inequality.

Citation format

WANG, Lidan; ZHAO, Yanhua. The concentration-compactness principle for the fractional laplacian on lattice graphs. Bulletin of the Malaysian Mathematical Sciences Society, 2026, 49(4).