A planar convex domain with many isolated ``hot spots on the boundary

DOI10.1007/s13160-012-0091-zzbMath1260.35090OpenAlexW2075568645MaRDI QIDQ1943091

Yasuhito Miyamoto

Publication date: 15 March 2013

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-012-0091-z

zbMATH Keywords

hot spotsconvex domainnodal linemaximum point

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items

The hot spots conjecture can be false: some numerical examples, Non-boundedness of the number of super level domains of eigenfunctions, Critical points of Laplace eigenfunctions on polygons, An upper bound on the hot spots constant, Location of hot spots in thin curved strips, Hot spots in convex domains are in the tips (up to an inradius), A spectral approach to the shortest path problem, Monotone properties of the eigenfunction of Neumann problems, On mixed Dirichlet-Neumann eigenvalues of triangles, Hot spots conjecture for a class of acute triangles, Erratum to: ``Euclidean triangles have no hot spots, On Courant’s Nodal Domain Property for Linear Combinations of Eigenfunctions Part II

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