A strong unique continuation property for weakly coupled elliptic systems

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-11-20 DOI:10.1016/j.jmaa.2024.129069

Mónica Clapp , Víctor Hernández-Santamaría , Alberto Saldaña

引用次数: 0

Abstract

We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system-structure of the problem and Carleman estimates. Then, we use our unique continuation theorems to show two nonexistence results. The first one states the nonexistence of nontrivial solutions to a weakly coupled elliptic system with a critical nonlinearity and Dirichlet boundary condition on starshaped domains, whereas the second one yields nonexistence of symmetric least energy solutions for a critical system in more general domains.

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弱耦合椭圆系统的强唯一延续特性

我们为弱耦合椭圆系统（包括竞争性椭圆系统）建立了强唯一延续性质的有效性。我们的证明利用了问题的系统结构和卡勒曼估计。然后，我们利用唯一续存定理证明了两个不存在结果。第一个结果表明，在星形域中，具有临界非线性和迪里希特边界条件的弱耦合椭圆系统的非微观解不存在，而第二个结果表明，在更一般的域中，临界系统的对称最小能量解不存在。

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

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.