GAGLIARDO-NIRENBERG-SOBOLEV INEQUALITIES ON PLANAR GRAPHS

被引：0
|
作者：
Esteban, Maria J. [1 ]
机构：
[1] PSL Res Univ, CEREMADE, CNRS, Univ Paris Dauphine, Pl Lattre Tassigny, F-75016 Paris, France
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2022年 / 21卷 / 06期
关键词：
Functional inequality; optimizer; extremal function; graph; planar graph; CONCENTRATION-COMPACTNESS PRINCIPLE; NONLINEAR ELLIPTIC-EQUATIONS; MONOTONICITY; CALCULUS; THEOREM; PERIOD;
D O I：
10.3934/cpaa.2022051
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study a family of the interpolation GagliardoNirenberg-Sobolev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities are achieved. The inequalities being equivalent to some minimization problems, we also analyse the set of solutions of the Euler-Lagrange equations satisfied by extremal functions, or equivalently, by minimizers.
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页码：2101 / 2114
页数：14
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