域上变指数Trudinger-Moser型泛函的紧性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-09-02 DOI:10.1016/j.jmaa.2025.130037

Masato Hashizume, Michinori Ishiwata, Xu Yan

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引用次数: 0

摘要

本文研究了几种变指数Trudinger-Moser型泛函的紧性。在变指数上建立了保证泛函紧性或非紧性的各种近似最优条件。我们在有界域和整个域上处理这个问题。整个域的情况需要排除目前尚未得到很好处理的所谓消失现象的条件，并考虑集中现象。

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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The compactness of Trudinger-Moser type functionals with variable exponents for domains in RN

In this paper, we consider the compactness property of several Trudinger-Moser type functionals with variable exponents. We establish various nearly optimal conditions on the variable exponents which assure the compactness or the noncompactness of functionals. We treat this problem both on bounded domains and the entire domain. The entire domain case needs the condition which excludes the so-called vanishing phenomena which has not been well treated so far together with the consideration of the concentration phenomena.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.