Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients

@article{Suslina2017HomogenizationOT,
  title={Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients},
  author={T. A. Suslina},
  journal={Complex Variables and Elliptic Equations},
  year={2017},
  volume={63},
  pages={1185 - 1215}
}
  • T. Suslina
  • Published 21 May 2017
  • Mathematics
  • Complex Variables and Elliptic Equations
Let be a bounded domain of class . In , we study a self-adjoint strongly elliptic operator of order 2p given by the expression , , with Neumann boundary conditions. Here, is a bounded and positive definite matrix-valued function in , periodic with respect to some lattice; is a differential operator of order p. The symbol is subject to some condition ensuring strong ellipticity of the operator . We find approximations for the resolvent in different operator norms with error estimates depending… 
Homogenization of higher-order parabolic systems in a bounded domain
ABSTRACT Let be a bounded domain of class . In , we consider matrix elliptic differential operators and of order 2p ( ) with the Dirichlet or Neumann boundary conditions, respectively. The
Convergence rates in homogenization of higher order parabolic systems
This paper is concerned with the optimal convergence rate in homogenization of higher order parabolic systems with bounded measurable, rapidly oscillating periodic coefficients. The sharp $O(\va)$
Convergence rates in almost-periodic homogenization of higher-order elliptic systems
This paper concentrates on the quantitative homogenization of higher-order elliptic systems with almost-periodic coefficients in bounded Lipschitz domains. For almost-periodic coefficients in the
On operator estimates in homogenization of non-local operators of convolution type
. The paper studies a bounded symmetric operator A ε in L 2 ( R d ) with here ε is a small positive parameter. It is assumed that a ( x ) is a non-negative L 1 ( R d ) function such that a ( − x ) =
Uniform boundary estimates in homogenization of higher-order elliptic systems
AbstractThis paper focuses on uniform boundary estimates in homogenization of a family of higher-order elliptic operators $$\mathcal {L}_\varepsilon $$Lε, with rapidly oscillating periodic

References

SHOWING 1-10 OF 47 REFERENCES
Homogenization of initial boundary value problems for parabolic systems with periodic coefficients
Let be a bounded domain of class . In the Hilbert space , we consider matrix elliptic second-order differential operators and with the Dirichlet or Neumann boundary condition on , respectively. Here
Homogenization of the elliptic Dirichlet problem: operator error estimates in $L_2$
Let O ⊂ R be a bounded domain of class C. In the Hilbert space L2(O;C ), we consider a matrix elliptic second order differential operator AD,ε with the Dirichlet boundary condition. Here ε > 0 is the
Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class ¹(ℝ^{})
Investigation of a class of matrix periodic elliptic second-order differential operators Aε in Rd with rapidly oscillating coefficients (depending on x/ε) is continued. The homogenization problem in
Homogenization of periodic differential operators of high order
A periodic differential operator of the form Aε = (Dp)∗g(x/ε)Dp is considered on L2(R); here g(x) is a positive definite symmetric tensor of order 2p periodic with respect to a lattice Γ. The
Homogenization with corrector term for periodic elliptic differential operators
We continue to study the class of matrix periodic elliptic differential operators Aε in Rd with coefficients oscillating rapidly (i.e., depending on x/ε). This class was introduced in the authors’
Operator estimates in homogenization theory
This paper gives a systematic treatment of two methods for obtaining operator estimates: the shift method and the spectral method. Though substantially different in mathematical technique and
HOMOGENIZATION OF THE DIRICHLET PROBLEM FOR ELLIPTIC SYSTEMS: ‐OPERATOR ERROR ESTIMATES
Let OR d be a bounded domain of class C 1,1 . In L2(O;C n ), we consider a matrix elliptic differential operator A" = b(D) � g(x/")b(D) with the Dirichlet boundary condition. We assume that an
Second order periodic differential operators. Threshold properties and homogenization
The vector periodic differential operators (DO’s) A admitting a factorization A = X ∗X , where X is a first order homogeneous DO, are considered in L2(R). Many operators of mathematical physics have
Convergence Rates in L2 for Elliptic Homogenization Problems
We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet
Homogenization of Differential Operators and Integral Functionals
1 Homogenization of Second Order Elliptic Operators with Periodic Coefficients.- 1.1 Preliminaries.- 1.2 Setting of the Homogenization Problem.- 1.3 Problems of Justification Further Examples.- 1.4
...
...