A singular Adams' inequality with logarithmic weights and applications

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-11-08 DOI:10.1080/00036811.2023.2279955

Shiqi Zhang

引用次数: 0

Abstract

AbstractIn this paper, we consider a singular Adams' inequality with logarithmic weights in the unit ball of R4. Our results extend the results of Zhu and Wang [Adams' inequality with logarithmic weights in R4. Proc Amer Math Soc. 2021;149(8):3463–3472] on Adams' inequality with logarithmic weights to singular case. Then, we study the existence of solutions for some weighted mean field equations, relying on variational methods and the singular Adams' inequality with logarithmic weights we previously established.Keywords: Singular Adams' inequalitylogarithmic weightsweighted mean field equations2010 Mathematics Subject Classifications: 35A2135A2335D3035J25 Disclosure statementNo potential conflict of interest was reported by the author(s).

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具有对数权值的奇异亚当斯不等式及其应用

摘要本文考虑R4单位球上的一个对数权的奇异Adams不等式。我们的结果推广了Zhu和Wang [Adams]不等式在R4中的对数权重的结果。[j] .数学学报，2011;49(8):3463-3472 .]然后，我们利用变分方法和之前建立的对数权的奇异亚当斯不等式，研究了一些加权平均场方程解的存在性。关键词:奇异亚当斯不等式对数加权均场方程数学学科分类:35A2135A2335D3035J25披露声明作者未报告潜在利益冲突。

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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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.