一类非局部奇异椭圆问题的比较结果

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Asymptotic Analysis Pub Date : 2023-11-10 DOI:10.3233/asy-231860

Barbara Brandolini, Ida de Bonis, Vincenzo Ferone, Bruno Volzone

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引用次数: 0

摘要

我们以质量浓度比较的形式给出了分数阶奇异椭圆方程在有界域中的对称结果，并与齐次外部狄利克雷条件耦合。根据方程右侧的可和性，给出了两种类型的比较结果。在主要结果的证明的核心中使用的最大原理论证提供了一种非标准的、灵活的替代方法。配给。动力机械。肛门239(2021)1733-1770，定理31)。一些有趣的结果是L - p正则性结果和解的非局部能量估计。

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Comparison results for a nonlocal singular elliptic problem

We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are presented, depending on the summability of the right-hand side of the equation. The maximum principle arguments employed in the core of the proofs of the main results offer a nonstandard, flexible alternative to the ones described in (Arch. Ration. Mech. Anal. 239 (2021) 1733–1770, Theorem 31). Some interesting consequences are L p regularity results and nonlocal energy estimates for solutions.

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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.