Sharp Gagliardo-Nirenberg inequality and logarithmic Sobolev inequality on integer lattices

2025/11/01 by Yongjie Shi, Shi, Yongjie, Chengjie Yu +1
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2511.00393

Abstract

In this paper, we obtain a sharp Garliardo-Nirenberg inequality on integer lattices and characterize its rigidity. Moreover, as a consequence of the sharp Garliardo-Nirenberg inequality, we obtain sharp logarithmic Sobolev inequalities on integer lattices.

Citations

• Ollivier curvature, Isoperimetry, concentration, and Log-Sobolev inequalitiy
• Sobolev spaces on locally finite graphs
• The existence of extremal functions for discrete Sobolev inequalities on lattice graphs

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