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- W3171242843 abstract "We introduce a new variational principle for the study of eigenvalues and eigenfunctions of the Laplacians with Neumann and Dirichlet boundary conditions on planar domains and apply it to the famous hot spots conjecture, which we prove for a large class of simply connected, not necessarily convex domains. We show that each eigenfunction of the Neumann Laplacian corresponding to the lowest positive eigenvalue is strictly monotonous along certain directions if the domain faces two opposite quadrants. In particular, the maximum and minimum of such an eigenfunction may only be located on the boundary." @default.
- W3171242843 created "2021-06-22" @default.
- W3171242843 creator A5055419536 @default.
- W3171242843 date "2021-06-09" @default.
- W3171242843 modified "2023-09-27" @default.
- W3171242843 title "A new approach to the hot spots conjecture" @default.
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