標題: Inequalities between Dirichlet and Neumann eigenvalues for domains in spheres
作者: Hsu, YJ
Wang, TH
應用數學系
Department of Applied Mathematics
關鍵字: Laplace-Beltrami operator;Dirichlet eigenvalue;Neumann eigenvalue
公開日期: 1-Dec-2001
摘要: Let M be a domain in the unit n-sphere with smooth boundary. The purpose of this paper is to describe some inequalities between Dirichlet and Neumann eigenvalues for M under certain convex restrictions on the boundary. We prove that if the mean curvature of the boundary is nonpositive, then the kth nonzero Neumann eigenvalue is less than or equal to the kth Dirichlet eigenvalue for k = 1, 2, Furthermore, if the second fundamental form of the boundary is nonpositive, then the (k + [n-1/2])th nonzero Neumann eigenvalue is less than or equal to the kth Dirichlet eigenvalue for k = 1, 2, (. . .).
URI: http://hdl.handle.net/11536/29205
ISSN: 1027-5487
期刊: TAIWANESE JOURNAL OF MATHEMATICS
Volume: 5
Issue: 4
起始頁: 755
結束頁: 766
Appears in Collections:Articles