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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.
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C. Judge and S. Mondal, Euclidean triangles have no hot spots
2020
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S. Steinerberger, Hot Spots in Convex Domains are in the Tips (up to an Inradius)
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A. Kleefeld, The hot spots conjecture can be false: Some numerical examples
2021
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F. Gesztesy and M. Mitrea, Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities
2009
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J. P. Kelliher, Eigenvalues of the Stokes operator versus the Dirichlet Laplacian in the plane
2010
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F. Gesztesy and M. Mitrea, A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains
2011
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C. Judge and S. Mondal, Erratum: Euclidean triangles have no hot spots
2022
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C. Judge and S. Mondal, Critical points of Laplace eigenfunctions on polygons
2022
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