Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients

General topics in linear spectral theory for PDEs (35P05) One-parameter semigroups and linear evolution equations (47D06) Schrödinger operator, Schrödinger equation (35J10) Initial value problems for second-order parabolic equations (35K15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Cites Work

On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition
Spectral approach to homogenization of nonstationary Schrödinger-type equations
Convergence rates in parabolic homogenization with time-dependent periodic coefficients
Convergence rates in $L ^{2}$ for elliptic homogenization problems
Periodic homogenization of elliptic systems
On operator estimates for some problems in homogenization theory
Estimates of homogenization for a parabolic equation with periodic coefficients
Estimates of locally periodic and reiterated homogenization for parabolic equations
On homogenization for non-self-adjoint locally periodic elliptic operators
Homogenization of the Dirichlet problem for elliptic and parabolic systems with periodic coefficients
Convergence rates and interior estimates in homogenization of higher order elliptic systems
Spectral approach to homogenization of hyperbolic equations with periodic coefficients
Interior error estimate for periodic homogenization
Correctors for the homogenization of the wave and heat equations
Operator estimates for elliptic problem with rapidly alternating Steklov boundary condition
Wildly perturbed manifolds: norm resolvent and spectral convergence
Homogenization of a non-stationary periodic Maxwell system in the case of constant permeability
Homogenization of the higher-order Schrödinger-type equations with periodic coefficients
Resolvent approximations in $L^2$-norm for elliptic operators acting in a perforated space
Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit
Homogenization of the higher-order hyperbolic equations with periodic coefficients
Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
On homogenization of locally periodic elliptic and parabolic operators
Quantitative estimates in reiterated homogenization
On resolvent approximations of elliptic differential operators with locally periodic coefficients
$L^2$-approximation of resolvents in homogenization of higher order elliptic operators
Homogenization for locally periodic elliptic operators
On operator error estimates for homogenization of hyperbolic systems with periodic coefficients
Approximation of the exponential of a diffusion operator with multiscale coefficients
Homogenization of the stationary Maxwell system with periodic coefficients in a bounded domain
On the homogenization of periodic hyperbolic systems
Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics
Operator estimates in reiterated and locally periodic homogenization
Uniform resolvent convergence for strip with fast oscillating boundary
On operator estimates in homogenization theory
On homogenization of periodic parabolic systems
Linear and quasilinear elliptic equations
Homogenization of the Schrödinger equation and effective mass theorems
Convergence rates in homogenization of Stokes systems
Homogenization of the fourth-order elliptic operator with periodic coefficients with correctors taken into account
Operator estimates for homogenization of the Robin Laplacian in a perforated domain
On operator estimates in homogenization of nonlocal operators of convolution type
Bloch Approximation in Homogenization and Applications
Homogenization of elliptic operators with periodic coefficients in dependence of the spectral parameter
Estimates in homogenization of higher-order elliptic operators
Homogenization of initial boundary value problems for parabolic systems with periodic coefficients
Convergence Rates for General Elliptic Homogenization Problems in Lipschitz Domains
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
Operator error estimates for homogenization of the elliptic Dirichlet problem in a bounded domain
Homogenization of the Cauchy problem for parabolic systems with periodic coefficients
Convergence rates in periodic homogenization of systems of elasticity
Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve
Periodic Homogenization of Nonlocal Operators with a Convolution-Type Kernel
Operator error estimates for homogenization of fourth order elliptic equations
Homogenization with corrector for a stationary periodic Maxwell system
Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients
Operator error estimates in the homogenization problem for nonstationary periodic equations
Homogenization in the Sobolev class $H^{1}(\mathbb R^{d})$ for second order periodic elliptic operators with the inclusion of first order terms
Homogenization of periodic differential operators of high order
Homogenization of high order elliptic operators with periodic coefficients
Homogenization of periodic parabolic systems in the $L_2(\mathbb {R}^d)$-norm with the corrector taken into account
Homogenization of a stationary periodic Maxwell system
Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev SpaceH¹(ℝ^d)
A periodic parabolic Cauchy problem: Homogenization with corrector
Homogenization with corrector term for periodic elliptic differential operators
AN ASYMPTOTIC EXPANSION OF THE SOLUTION OF A SECOND ORDER ELLIPTIC EQUATION WITH PERIODIC RAPIDLY OSCILLATING COEFFICIENTS
Homogenization of the first initial boundary-value problem for parabolic systems: operator error estimates
Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients
Spectral Approach to Homogenization of Elliptic Operators in a Perforated Space
Homogenization of higher-order parabolic systems in a bounded domain
Operator estimates for the crushed ice problem
Norm-resolvent convergence in perforated domains
Error estimate and unfolding for periodic homogenization
Second order periodic differential operators. Threshold properties and homogenization
Homogenization of hyperbolic equations with periodic coefficients in ℝ^{𝕕}: Sharpness of the results
Operator error estimates for homogenization of the nonstationary Schrödinger-type equations: sharpness of the results
Threshold approximations for the resolvent of a polynomial nonnegative operator pencil
Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations
Homogenization of periodic Schrödinger-type equations, with lower order terms
Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition
Homogenization of elliptic systems with periodic coefficients: operator error estimates in $L_2(\mathbb {R}^d)$ with corrector taken into account
On ground state of some non local Schrödinger operators
HOMOGENIZATION OF THE DIRICHLET PROBLEM FOR ELLIPTIC SYSTEMS: ‐OPERATOR ERROR ESTIMATES
Threshold approximations for a factorized selfadjoint operator family with the first and second correctors taken into account
Homogenization of the Neumann Problem for Elliptic Systems with Periodic Coefficients
Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class $H^1({\mathbb{R}}^d)$
Threshold approximations with corrector for the resolvent of a factorized selfadjoint operator family
On the structure of the lower edge of the spectrum of the periodic magnetic Schrödinger operator with small magnetic potential
Homogenization of a stationary periodic Maxwell system in a bounded domain in the case of constant magnetic permeability
Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients
Approximation of resolvents in homogenization of fourth-order elliptic operators
Resolvent estimates for high-contrast elliptic problems with periodic coefficients
Homogenization for Locally Periodic Elliptic Problems on a Domain
Improved resolvent 𝐿²-approximations in homogenization of fourth order operators
Spectrum of a convolution operator with potential
Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems
Homogenization of the higher-order parabolic equations with periodic coefficients
On homogenization for piecewise locally periodic operators
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