The existence of extremal functions for discrete Sobolev inequalities on lattice graphs
Analysis of PDEs
2021-07-01 v1
Abstract
In this paper, we study the existence of extremal functions of the discrete Sobolev inequality and Hardy-Littlewood-Sobolev inequality on lattice graphs. We introduce the discrete Concentration-Compactness principle, and prove the existence of extremal functions for the best constants in the supercritical cases.
Keywords
Cite
@article{arxiv.2106.15982,
title = {The existence of extremal functions for discrete Sobolev inequalities on lattice graphs},
author = {Bobo Hua and Ruowei Li},
journal= {arXiv preprint arXiv:2106.15982},
year = {2021}
}
Comments
16 pages