The eigenvalues of the Laplacian with Dirichlet boundary condition in \(\mathbb {R}^2\) are almost never minimized by disks

DOI10.1007/s10455-014-9446-9zbMath1346.35133OpenAlexW1986345804MaRDI QIDQ2017597

Amandine Berger

Publication date: 23 March 2015

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-014-9446-9

zbMATH Keywords

eigenvaluesminimizationLaplaciandisksDirichlet

Mathematics Subject Classification ID

Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Variational methods for eigenvalues of operators (49R05)

Related Items (12)

TRIANGLES CAPTURING MANY LATTICE POINTS ⋮ Eigenvalues of Dirichlet Laplacian within the class of open sets with constant diameter ⋮ A combined finite element and Bayesian optimization framework for shape optimization in spectral geometry ⋮ Bounds and extremal domains for Robin eigenvalues with negative boundary parameter ⋮ Asymptotic behaviour of cuboids optimising Laplacian eigenvalues ⋮ MINIMIZING DIRICHLET EIGENVALUES ON CUBOIDS OF UNIT MEASURE ⋮ Eigenvalue Optimisation on Flat Tori and Lattice Points in Anisotropically Expanding Domains ⋮ Minimization of the Eigenvalues of the Dirichlet-Laplacian with a Diameter Constraint ⋮ Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint ⋮ Maximising Neumann eigenvalues on rectangles ⋮ Extremal p -Laplacian eigenvalues ⋮ Steklov eigenvalues of reflection-symmetric nearly circular planar domains

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