Operator estimates in homogenization theory
From MaRDI portal
Publication:2832508
DOI10.1070/RM9710zbMath1354.35028MaRDI QIDQ2832508
S. E. Pastukhova, Vasilii V. Jikov
Publication date: 11 November 2016
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
periodicityspectral methodshift methodasymptotics of the fundamental solutionSteklov smoothingBloch representation of an operatorintegrated estimateNash-Aronson estimateproblem on the cell
Second-order elliptic equations (35J15) Initial value problems for second-order parabolic equations (35K15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Higher-order elliptic equations (35J30)
Related Items (71)
Homogenization of the higher-order hyperbolic equations with periodic coefficients ⋮ Norm resolvent convergence of elliptic operators in domains with thin spikes ⋮ Operator error estimates for homogenization of the nonstationary Schrödinger-type equations: sharpness of the results ⋮ Estimates of homogenization for the Beltrami equation ⋮ Improved approximations of resolvents in homogenization of higher order operators. The selfadjoint case ⋮ The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes ⋮ Localized modes due to defects in high contrast periodic media via two-scale homogenization ⋮ On Sobolev inequalities on singular and combined structures ⋮ Estimates for the locally periodic homogenization of the Riemann-Hilbert problem for a generalized Beltrami equation ⋮ Homogenization estimates in the Riemann-Hilbert problem for the general Beltrami equation on the plane ⋮ Homogenization of the fourth-order elliptic operator with periodic coefficients with correctors taken into account ⋮ On operator-type homogenization estimates for elliptic equations with lower order terms ⋮ Homogenization of the first initial boundary-value problem for parabolic systems: operator error estimates ⋮ Multiplication of distributions and algebras of mnemofunctions ⋮ Operator estimates for homogenization of the Robin Laplacian in a perforated domain ⋮ On resolvent approximations of elliptic differential operators with periodic coefficients ⋮ Operator estimates in homogenization of elliptic systems of equations ⋮ \(L^2\)-estimates for homogenization of elliptic operators ⋮ On operator estimates of the homogenization of higher-order elliptic systems ⋮ Homogenization for Locally Periodic Elliptic Problems on a Domain ⋮ Second-Order Homogenization of Periodic Schrödinger Operators with Highly Oscillating Potentials ⋮ Improved resolvent 𝐿²-approximations in homogenization of fourth order operators ⋮ \(L^2\)-estimates for homogenization of diffusion operators with unbounded nonsymmetric matrices ⋮ Homogenization of hyperbolic equations: operator estimates with correctors taken into account ⋮ High-energy homogenization of a multidimensional nonstationary Schrödinger equation ⋮ Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems ⋮ Homogenization estimates for parabolic equations with correctors ⋮ Homogenization of the higher-order parabolic equations with periodic coefficients ⋮ On operator estimates in homogenization of nonlocal operators of convolution type ⋮ Operator estimates for the Neumann sieve problem ⋮ Homogenization estimates of nondivergence elliptic operators of second order ⋮ Homogenization for operators with arbitrary perturbations in coefficients ⋮ Operator error estimates for homogenization of hyperbolic equations ⋮ Homogenization of a nonstationary model equation of electrodynamics ⋮ Large-time asymptotics of fundamental solutions for diffusion equations in periodic media and its application to averaging-theory estimates ⋮ Homogenization of the Schrödinger-type equations: operator estimates with correctors ⋮ Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients ⋮ On resolvent approximations of elliptic differential operators with locally periodic coefficients ⋮ Spectral approach to homogenization of hyperbolic equations with periodic coefficients ⋮ Improved resolvent approximations in homogenization of second-order operators with periodic coefficients ⋮ Spectral Approach to Homogenization of Elliptic Operators in a Perforated Space ⋮ Sobolev-Zygmund solutions for nonlinear elliptic equations with growth coefficients in \textit{BMO} ⋮ Homogenization estimates for singularly perturbed operators ⋮ \(L^2\)-approximation of resolvents in homogenization of higher order elliptic operators ⋮ Homogenization of periodic Schrödinger-type equations, with lower order terms ⋮ Homogenization of higher-order parabolic systems in a bounded domain ⋮ An optimal control problem for some nonlinear elliptic equations with unbounded coefficients ⋮ Homogenization of periodic parabolic systems in the $L_2(\mathbb {R}^d)$-norm with the corrector taken into account ⋮ On homogenization of the first initial-boundary value problem for periodic hyperbolic systems ⋮ Homogenization for locally periodic elliptic operators ⋮ Weak and strong approximation of semigroups on Hilbert spaces ⋮ Effective description of anisotropic wave dispersion in mechanical band-gap metamaterials via the relaxed micromorphic model ⋮ Improved approximations of resolvent in homogenization of higher order operators ⋮ On operator error estimates for homogenization of hyperbolic systems with periodic coefficients ⋮ Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations ⋮ 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 ⋮ Note on quantitative homogenization results for parabolic systems in \(\mathbb{R}^d\) ⋮ Improved approximations of resolvents in homogenization of fourth order operators ⋮ Convergence rates on periodic homogenization of \(p\)-Laplace type equations ⋮ On a pore-scale stationary diffusion equation: scaling effects and correctors for the homogenization limit ⋮ 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 ⋮ Elliptic operators in multidimensional cylinders with frequently alternating boundary conditions along a given curve ⋮ Accretivity of the general second order linear differential operator ⋮ Homogenization of the stationary Maxwell system with periodic coefficients in a bounded domain ⋮ Resolvent approximations in \(L^2\)-norm for elliptic operators acting in a perforated space ⋮ Approximations of resolvents of second order elliptic operators with periodic coefficients ⋮ Homogenization of hyperbolic equations with periodic coefficients in ℝ^{𝕕}: Sharpness of the results ⋮ Approximation of resolvents in homogenization of fourth-order elliptic operators ⋮ Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap
This page was built for publication: Operator estimates in homogenization theory