Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach

DOI10.1002/mma.2933zbMath1301.35065OpenAlexW1997696535MaRDI QIDQ2922228

Serhii V. Gryshchuk, Massimo Lanza de Cristoforis

Publication date: 9 October 2014

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2933

zbMATH Keywords

Laplace operatorSteklov eigenvaluessingularly perturbed domainreal analytic continuation

Mathematics Subject Classification ID

Systems of singular linear integral equations (45F15) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Estimates of eigenvalues in context of PDEs (35P15) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (8)

Strong convergence of a linearization method for semi-linear elliptic equations with variable scaled production ⋮ On eigenelements of a two-dimensional Steklov-type boundary value problem for the Lamé operator ⋮ Asymptotic behavior of the solutions of a transmission problem for the Helmholtz equation: A functional analytic approach ⋮ Mixed boundary value problems in singularly perturbed two-dimensional domains with the Steklov spectral condition ⋮ From Steklov to Neumann via homogenisation ⋮ Optimization of Steklov-Neumann eigenvalues ⋮ On the behavior of the spectrum of a perturbed Steklov boundary value problem with a weak singularity ⋮ Multiple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A real analyticity result for a nonlinear integral operator
• Simple Neumann eigenvalues for the Laplace operator in a domain with a small hole
• Real analytic families of harmonic functions in a domain with a small hole
• Two-scale convergence of Stekloff eigenvalue problems in perforated domains
• On the spectrum of the Steklov problem in a domain with a peak
• Asymptotics of the solution of the Steklov spectral problem in a domain with a blunted peak
• Homogenization of eigenvalue problems in perforated domains
• Asymptotic expansions of eigenvalues and eigenfunctions for elliptic boundary-value problems with rapidly oscillating coefficients in a perforated cube
• Steklov problems in perforated domains with a coefficient of indefinite sign
• Real analytic dependence of simple and double layer potentials upon perturbation of the support and of the density
• A singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain. A functional analytic approach
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Asymptotic behaviour of the solutions of a non-linear transmission problem for the Laplace operator in a domain with a small hole. A functional analytic approach
• Elliptic Partial Differential Equations of Second Order
• Microscopically weakly singularly perturbed loads for a nonlinear traction boundary value problem: a functional analytic approach
• Asymptotic behavior of the solutions of a nonlinear Robin problem for the Laplace operator in a domain with a small hole: a functional analytic approach
• Asymptotic Behavior of Stekloff Eigenvalues and Eigenfunctions

This page was built for publication: Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach