具有CKN算子的椭圆型问题的定性性质

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2023-01-01 DOI:10.2206/kyushujm.77.385

Huyuan CHEN, Yishan ZHENG

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引用次数: 1

摘要

研究了一类由两个自由参数控制的具有临界梯度和临界Hardy项的退化算子的基本性质。该算子由临界卡法瑞利-科恩-尼伦伯格不等式产生。利用相关泊松问题在包含原点的有界域上的孤立奇异解分类，分析了一类加权分布恒等式的基本解，得到了一类带该算子的Lane-Emden方程的Liouville定理。

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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QUALITATIVE PROPERTIES FOR ELLIPTIC PROBLEMS WITH CKN OPERATORS

The purpose of this paper is to study the basic properties of a degenerate operator with critical gradient and critical Hardy term, controlled by two free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of singular solutions with isolated singularities of the related Poisson problem in a bounded domain containing the origin.

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.