Sharp Gagliardo-Nirenberg inequality and logarithmic Sobolev inequality on integer lattices
Analysis of PDEs
2025-11-04 v1 Combinatorics
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.
Cite
@article{arxiv.2511.00393,
title = {Sharp Gagliardo-Nirenberg inequality and logarithmic Sobolev inequality on integer lattices},
author = {Yongjie Shi and Chengjie Yu},
journal= {arXiv preprint arXiv:2511.00393},
year = {2025}
}