Hadamard's formula inside and out

DOI10.1007/s10957-010-9681-6zbMath1209.49006OpenAlexW2079887183MaRDI QIDQ613580

Pavel Grinfeld

Publication date: 21 December 2010

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-010-9681-6

zbMATH Keywords

shape optimizationboundary perturbations of partial differential equationscalculus of moving surfacesHadamard's formula

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (23)

Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators ⋮ On a Classical Spectral Optimization Problem in Linear Elasticity ⋮ Continuous adjoint methods for turbulent flows, applied to shape and topology optimization: industrial applications ⋮ Hadamard-type formulas via the Maslov form ⋮ On Rayleigh's formula for the first Dirichlet eigenvalue of a radial perturbation of a ball ⋮ Domain dependence of eigenvalues of elliptic type operators ⋮ Stability of spectral partitions and the Dirichlet-to-Neumann map ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ Resolvent expansions for self‐adjoint operators via boundary triplets ⋮ Critical partitions and nodal deficiency of billiard eigenfunctions ⋮ Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error analysis ⋮ Second domain variation for problems with Robin boundary conditions ⋮ Variation de forme pour une équation instationnaire du 4ème ordre dans un modèle de dislocations ⋮ Laplace eigenvalues on regular polygons: a series in \(1/N\) ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories ⋮ An index theorem for Schrödinger operators on metric graphs ⋮ A localized domain perturbation which splits the spectrum of the Laplacian ⋮ On the Behavior of Clamped Plates under Large Compression ⋮ Thermodynamic forces in single crystals with dislocations ⋮ On eigenvalue asymptotics for strong δ-interactions supported by surfaces with boundaries ⋮ Hadamard asymptotics for eigenvalues of the Dirichlet Laplacian ⋮ Analytical and numerical assessments of boundary variations in Steklov eigenvalue problems ⋮ Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

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