Minimization of the third eigenvalue of the Dirichlet Laplacian

DOI10.1098/rspa.2000.0546zbMath0974.35082OpenAlexW2065550047MaRDI QIDQ4521624

Dorin Bucur, Antoine Henrot

Publication date: 12 December 2001

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

Full work available at URL: https://doi.org/10.1098/rspa.2000.0546

zbMATH Keywords

variational methodseigenvalue problemsmembrane vibrations

Mathematics Subject Classification ID

Related Items (18)

Extremum problems of Laplacian eigenvalues and generalized Polya conjecture ⋮ Recent Existence Results for Spectral Problems ⋮ Existence of minimizers for spectral problems ⋮ On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues ⋮ On the minimization of Dirichlet eigenvalues of the Laplace operator ⋮ On the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians ⋮ Rearrangement inequalities and applications to isoperimetric problems for eigenvalues ⋮ Spectral optimization problems ⋮ Numerical optimization of low eigenvalues of the Dirichlet and Neumann laplacians ⋮ Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian ⋮ An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift ⋮ The eigenvalues of the Laplacian with Dirichlet boundary condition in \(\mathbb {R}^2\) are almost never minimized by disks ⋮ Optimal measures for the fundamental gap of Schrödinger operators ⋮ Shape optimization towards stability in constrained hydrodynamic systems ⋮ Uniform concentration-compactness for Sobolev spaces on variable domains ⋮ On the inverse spectral problem for Euclidean triangles ⋮ Extremal p -Laplacian eigenvalues ⋮ Symmetrization of functions and principal eigenvalues of elliptic operators

This page was built for publication: Minimization of the third eigenvalue of the Dirichlet Laplacian