On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian

DOI10.1098/rspa.2010.0444zbMath1228.35156OpenAlexW2002283548MaRDI QIDQ3104820

Pedro R. S. Antunes, Antoine Henrot

Publication date: 17 December 2011

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2010.0444

zbMATH Keywords

eigenvaluesshape optimizationDirichlet-LaplacianNeumann-Laplacian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for eigenvalues of operators (49R05)

Related Items

Parametric shape optimization using the support function ⋮ Behaviour of inradius, circumradius, and diameter in generalized Minkowski spaces ⋮ On the boundary of the attainable set of the Dirichlet spectrum ⋮ On some isoperimetric inequalities involving eigenvalues of symmetric free membranes ⋮ A comparison between Neumann and Steklov eigenvalues ⋮ Some inequalities involving eigenvalues of the Neumann Laplacian ⋮ Blaschke--Santaló Diagram for Volume, Perimeter, and First Dirichlet Eigenvalue ⋮ Numerical shape optimization among convex sets ⋮ On Blaschke-Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue

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