Higher Order Convergence Rates in Theory of Homogenization I: Equations of Non-divergence Form

Abstract

We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.

Cited by in corpus (10)

• Optimal convergence rates for elliptic homogenization problems in nondivergence-form: analysis and numerical illustrations
• Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form
• Computational multiscale methods for nondivergence-form elliptic partial differential equations
• Higher Order Convergence Rates in Theory of Homogenization II: Oscillatory Initial Data
• Homogenization of nondivergence-form elliptic equations with discontinuous coefficients and finite element approximation of the homogenized problem
• Higher-order boundary layers and regularity for Stokes systems over rough boundaries
• Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations
• Finite element approximation of stationary Fokker--Planck--Kolmogorov equations with application to periodic numerical homogenization
• Uniform Integrability in Periodic Homogenization of Fully Nonlinear Equations
• Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form