The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes

DOI10.1007/s10958-018-3873-2zbMath1403.35023OpenAlexW2805126680MaRDI QIDQ1661607

A. I. Mukhametrakhimova, Denis I. Borisov

Publication date: 16 August 2018

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3873-2

zbMATH Keywords

convergence estimatesnorm resolvent convergencedimension-dependent convergence estimateselliptic equations with small wholes

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25)

Related Items (11)

Norm resolvent convergence of elliptic operators in domains with thin spikes ⋮ Bifurcations of essential spectra generated by a small non-Hermitian hole. I: Meromorphic continuations ⋮ Spectral convergence of the Laplace operator with Robin boundary conditions on a small hole ⋮ Approximation of point interactions by geometric perturbations in two-dimensional domains ⋮ Magnetic Neumann Laplacian on a domain with a hole ⋮ On a model graph with a loop and small edges. Holomorphy property of resolvent ⋮ Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum ⋮ On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary ⋮ Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition ⋮ Elliptic operators in multidimensional cylinders with frequently alternating boundary conditions along a given curve ⋮ Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge

Cites Work

• Unnamed Item
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• Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold
• On a waveguide with an infinite number of small windows
• On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition
• Operator estimates in nonlinear problems of reiterated homogenization
• Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows
• Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics
• Uniform resolvent convergence for strip with fast oscillating boundary
• On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes
• On operator estimates in homogenization theory
• The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization
• Operator estimates in homogenization theory
• Homogenization of parabolic and elliptic periodic operators in $L_2(\mathbb {R}^d)$ with the first and second correctors taken into account
• Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve
• Operator error estimates for homogenization of fourth order elliptic equations
• Homogenization of the planar waveguide with frequently alternating boundary conditions
• ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLES
• A BOUNDARY VALUE PROBLEM FOR THE ELLIPTIC EQUATION OF SECOND ORDER IN A DOMAIN WITH A NARROW SLIT. 1. THE TWO-DIMENSIONAL CASE
• A BOUNDARY VALUE PROBLEM FOR THE SECOND ORDER ELLIPTIC EQUATION IN A DOMAIN WITH A NARROW SLIT. 2. DOMAIN WITH A SMALL CAVITY
• Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients
• Second order periodic differential operators. Threshold properties and homogenization
• On homogenization procedure for periodic operators near the edge of an internal gap
• Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class $H^1({\mathbb{R}}^d)$

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