Asymptotic behaviour of optimal spectral planar domains with fixed perimeter

DOI10.1063/1.4803140zbMath1290.35164OpenAlexW2056211552MaRDI QIDQ5402280

Dorin Bucur, Pedro Freitas

Publication date: 6 March 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4803140

zbMATH Keywords

asymptotic behaviour\(k\)th Dirichlet eigenvalueoptimal spectral planar domains

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (15)

Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction ⋮ TRIANGLES CAPTURING MANY LATTICE POINTS ⋮ Shifted lattices and asymptotically optimal ellipses ⋮ Bounds and extremal domains for Robin eigenvalues with negative boundary parameter ⋮ Asymptotic behaviour of extremal averages of Laplacian eigenvalues ⋮ MINIMIZING DIRICHLET EIGENVALUES ON CUBOIDS OF UNIT MEASURE ⋮ Maximization of the Steklov Eigenvalues With a Diameter Constraint ⋮ On the minimization of Dirichlet eigenvalues ⋮ Minimization of the Eigenvalues of the Dirichlet-Laplacian with a Diameter Constraint ⋮ Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles ⋮ Existence and regularity of minimizers for some spectral functionals with perimeter constraint ⋮ Shapes of drums with lowest base frequency under non-isotropic perimeter constraints ⋮ Maximising Neumann eigenvalues on rectangles ⋮ Extremal p -Laplacian eigenvalues ⋮ Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains

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