English

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.

Keywords

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}
}