Robin和Dirichlet特征值的尺度不等式和极限

IF 1.2 3区 数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2024-11-26 DOI:10.1016/j.jmaa.2024.129082
Scott Harman
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引用次数: 0

摘要

对于球面和双曲空间的拉普拉斯算子,二维的Robin特征值和高维的Dirichlet特征值满足类似于欧几里德拉普拉斯算子标准尺度不变量的尺度不等式。这些结果将Langford和Laugesen的工作推广到高维的Robin问题和Dirichlet问题。此外,当定义域扩展到2球时,尺度Robin特征值表现出奇异性,趋向于外部Robin问题的谱。
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Scaling inequalities and limits for Robin and Dirichlet eigenvalues
For the Laplacian in spherical and hyperbolic spaces, Robin eigenvalues in two dimensions and Dirichlet eigenvalues in higher dimensions are shown to satisfy scaling inequalities analogous to the standard scale invariance of the Euclidean Laplacian. These results extend work of Langford and Laugesen to Robin problems and to Dirichlet problems in higher dimensions. In addition, scaled Robin eigenvalues behave exotically as the domain expands to a 2-sphere, tending to the spectrum of an exterior Robin problem.
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CiteScore
2.50
自引率
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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.
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