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- W1840765890 abstract "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 $k$th nonzero Neumann eigenvalue is less than or equal to the $k$th Dirichlet eigenvalue for $k=1, 2,cdots$. Furthermore, if the second fundamental form of the boundary is nonpositive, then the $(k+left[frac{n-1}{2}right])$th nonzero Neumann eigenvalue is less than or equal to the $k$th Dirichlet eigenvalue for $k=1,2,cdots$." @default.
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- W1840765890 date "2001-12-01" @default.
- W1840765890 modified "2023-09-25" @default.
- W1840765890 title "INEQUALITIES BETWEEN DIRICHLET AND NEUMANN EIGENVALUES FOR DOMAINS IN SPHERES" @default.
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- W1840765890 doi "https://doi.org/10.11650/twjm/1500574993" @default.
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