A Discrete Sobolev Inequality on Lattices
Year: 2026
Type: article
Abstract: Recently Hamamuki proved an optimal isoperimetric inequality with constraint in an \(n\)-dimensional lattice. The main idea of the proof is based on the ABP method, which was used by Cabré to give a new proof of the classical isoperimetric inequality. In this paper we generalize Hamamuki’s isoperimetric inequality to a Sobolev inequality by using Brendle’s new ideas.
Source: Journal of Mathematical Study
Author: Xuzhou Ren
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7225610988