二维球面上的一类插值不等式

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2023-01-01 DOI:10.4213/sm9786e

Sergey Vital'evich Zelik, Aleksei Andreevich Ilyin

引用次数: 0

摘要

在二维球面上证明了Sobolev空间$H^1$中正交函数系统和无散度向量函数系统的$L^p$ -范数的估计。作为推论，在Gagliardo-Nirenberg插值不等式中得到了嵌入的阶锐常数$H^1\hookrightarrow L^q$, $q<\infty$。参考书目:25篇。

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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On a class of interpolation inequalities on the 2D sphere

We prove estimates for the $L^p$-norms of systems of functions and divergence-free vector functions that are orthonormal in the Sobolev space $H^1$ on the 2D sphere. As a corollary, order sharp constants for the embedding $H^1\hookrightarrow L^q$, $q<\infty$, are obtained in the Gagliardo-Nirenberg interpolation inequalities. Bibliography: 25 titles.

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis