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

Yongjie Shi; Chengjie Yu

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arXiv · 2511.00393

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

Yongjie Shi·Chengjie Yu

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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.

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Yongjie Shi, Chengjie Yu. 2025-11-01. Sharp Gagliardo-Nirenberg inequality and logarithmic Sobolev inequality on integer lattices. https://arxiv.org/abs/2511.00393

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