Second domain variation for problems with Robin boundary conditions

DOI10.1007/s10957-015-0801-1zbMath1329.49082arXiv1403.2220OpenAlexW1120173657MaRDI QIDQ896179

Catherine Bandle, Alfred Wagner

Publication date: 14 December 2015

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

Full work available at URL: https://arxiv.org/abs/1403.2220

zbMATH Keywords

Steklov eigenvalue problemoptimal domainfirst domain variationRobin boundary value problemsecond domain variation

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Estimates of eigenvalues in context of PDEs (35P15) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Variational methods for second-order elliptic equations (35J20) Variational methods for eigenvalues of operators (49R05) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Related Items (14)

Optimality conditions of the first eigenvalue of a fourth order Steklov problem ⋮ Some properties of the torsion function with Robin boundary conditions ⋮ Hadamard-type formulas via the Maslov form ⋮ Resolvent expansions for self‐adjoint operators via boundary triplets ⋮ Second domain variation for problems with Robin boundary conditions ⋮ Domain perturbations for elliptic problems with Robin boundary conditions of opposite sign ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories ⋮ Symmetry for a general class of overdetermined elliptic problems ⋮ A localized domain perturbation which splits the spectrum of the Laplacian ⋮ Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues ⋮ Simulation of Multiscale Hydrophobic Lipid Dynamics via Efficient Integral Equation Methods ⋮ Stability analysis of the two-phase torsional rigidity near a radial configuration ⋮ Stability analysis on two thermal insulation problems ⋮ Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

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