Upper and lower bounds for the first Dirichlet eigenvalue of a triangle

DOI10.1090/S0002-9939-06-08339-0zbMath1092.35070MaRDI QIDQ3376971

Pedro Freitas

Publication date: 27 March 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

isoperimetric inequalityeigenfunctionDirichlet Laplaciantest function

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains ⋮ Families of non-tiling domains satisfying Pólya’s conjecture ⋮ Sums of Laplace eigenvalues-rotationally symmetric maximizers in the plane ⋮ Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi ⋮ Sharp bounds for eigenvalues of triangles ⋮ Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals ⋮ Maximizing Neumann fundamental tones of triangles ⋮ An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit ⋮ Minimizing Neumann fundamental tones of triangles: an optimal Poincaré inequality ⋮ SHARP CONSTANTS IN THE POINCARÉ, STEKLOV AND RELATED INEQUALITIES (A SURVEY)

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