Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities

详细信息    查看全文

• 作者：Fritz Gesztesy ; Marius Mitrea
• 关键词：Lipschitz domains ; Nonlocal Robin Laplacians ; Spectral analysis ; Eigenvalue inequalities
• 刊名：Journal of Differential Equations
• 出版年：2009
• 出版时间：15 November 2009
• 年：2009
• 卷：247
• 期：10
• 页码：2871-2896
• 全文大小：308 K

文摘

The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators Θ which give rise to self-adjoint Laplacians −Δ_Θ,Ω in L²(Ω;dⁿx) with (nonlocal and local) Robin-type boundary conditions on bounded Lipschitz domains , , n2. Second, we extend Friedlander's inequalities between Neumann and Dirichlet Laplacian eigenvalues to those between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with bounded Lipschitz domains Ω, following an approach introduced by Filonov for this type of problems.