Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems

DOI10.1051/cocv/2021033zbMath1481.65218arXiv2007.15033OpenAlexW3136231698MaRDI QIDQ4999532

Edouard Oudet, Braxton Osting, Chiu-Yen Kao

Publication date: 7 July 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.15033

zbMATH Keywords

eigenvalue optimizationfree boundary minimal surfaceSteklov eigenvalue

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Ill-posed problems for PDEs (35R25) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (5)

Numerical calculation of extremal Steklov eigenvalues in 3D and 4D ⋮ Harmonic Functions on Finitely Connected Tori ⋮ Extremal Graph Realizations and Graph Laplacian Eigenvalues ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Large Steklov eigenvalues via homogenisation on manifolds

Uses Software

• KNITRO

Cites Work

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• An extremal eigenvalue problem for the Wentzell-Laplace operator
• Sharp eigenvalue bounds and minimal surfaces in the ball
• Extremal problems for Steklov eigenvalues on annuli
• Optimization of spectral functions of Dirichlet-Laplacian eigenvalues
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Upper bounds for Steklov eigenvalues on surfaces
• Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds
• Numerical optimization of low eigenvalues of the Dirichlet and Neumann laplacians
• Some results on higher eigenvalue optimization
• Minimal convex combinations of three sequential Laplace-Dirichlet eigenvalues
• Maximal convex combinations of sequential Steklov eigenvalues
• Spectral geometry of the Steklov problem (survey article)
• Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
• Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint
• Minimal Convex Combinations of Sequential Laplace--Dirichlet Eigenvalues
• Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues
• Maximization of Laplace−Beltrami eigenvalues on closed Riemannian surfaces
• Sums of reciprocal Stekloff eigenvalues
• Conformal Geometry
• SERIES SOLUTION OF LAPLACE PROBLEMS
• Numerical Minimization of Dirichlet Laplacian Eigenvalues of Four-Dimensional Geometries
• Computational Methods for Extremal Steklov Problems
• Numerical minimization of eigenmodes of a membrane with respect to the domain
• Minimal surfaces and eigenvalue problems
• Optimal Shapes Maximizing the Steklov Eigenvalues
• Steklov eigenvalues and quasiconformal maps of simply connected planar domains

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