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

DOI10.1080/17476930902999058zbMath1241.35049OpenAlexW4249117414MaRDI QIDQ3406624

Massimo Lanza de Cristoforis

Publication date: 19 February 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930902999058

zbMATH Keywords

Laplace operatorreal analytic continuation in Banach spacesingularly perturbed domainnon-linear transmission problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Systems of singular linear integral equations (45F15) Boundary value problems for second-order elliptic equations (35J25) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (16)

The Dirichlet problem in a planar domain with two moderately close holes ⋮ Shape analyticity and singular perturbations for layer potential operators ⋮ Existence results for a nonlinear nonautonomous transmission problem via domain perturbation ⋮ A mixed problem for the Laplace operator in a domain with moderately close holes ⋮ A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary ⋮ Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach ⋮ A real analyticity result for a nonlinear integral operator ⋮ Asymptotic behavior of the solutions of a transmission problem for the Helmholtz equation: A functional analytic approach ⋮ Real analytic families of harmonic functions in a domain with a small hole ⋮ The functional analytic approach for quasi-periodic boundary value problems for the Helmholtz equation ⋮ A quasi-linear heat transmission problem in a periodic two-phase dilute composite. A functional analytic approach ⋮ Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem ⋮ A tribute to Massimo Lanza de Cristoforis ⋮ A singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain. A functional analytic approach ⋮ A singularly perturbed nonlinear traction problem in a periodically perforated domain: a functional analytic approach ⋮ Existence results for a nonlinear transmission problem

Cites Work

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• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
• 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
• The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity
• A domain perturbation problem for the Poisson equation
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