Improved approximations of resolvents in homogenization of fourth-order operators with periodic coefficients

2021/04/12 by Pastukhova, Svetlana
#35J30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.05749

Abstract

In the whole space R^d, d≥ 2, we study homogenization of a divergence form elliptic fourth-order operator A_ε with measurable ε-periodic coefficients, where ε is a small parameter. For the resolvent (A_ε+1)^-1, acting as an operator from L² to H², we find an approximation with remainder term of order O(ε²) as ε tends to 0. Relying on this result, we construct the resolvent approximation with remainder of order O(ε³) in the operator L²-norm. We employ two-scale expansions that involve smoothing.

Related

• Homogenization estimates for high order elliptic operators
• Improved homogenization estimates for high order elliptic systems
• Operator perturbation for fourth order elliptic equations with variable coefficients
• Uniform Estimates of Resolvents in Homogenization Theory of Elliptic Systems
• Homogenization of high order elliptic operators with periodic coefficients