平面图上的Gagliardo-Nirenberg-Sobolev不等式

Communications on Pure & Applied Analysis Pub Date : 2021-10-14 DOI:10.3934/cpaa.2022051

M. Esteban

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引用次数: 1

摘要

本文研究了平面图上的一类插值Gagliardo-Nirenberg-Sobolev不等式。我们感兴趣的是知道不等式中的最佳常数是什么时候得到的。由于不等式等价于一些最小化问题，我们还分析了由极值函数或等效的最小化器满足的欧拉-拉格朗日方程的解集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Gagliardo-Nirenberg-Sobolev inequalities on planar graphs

In this paper we study a family of the interpolation Gagliardo-Nirenberg-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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Communications on Pure & Applied Analysis

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