HOMOGENIZATION ESTIMATES FOR HIGH-ORDER ELLIPTIC OPERATORS
Svetlana Evgenievna Pastukhova · Functional Differential Equations · 2026
In the whole space Rd (d ≥ 2), we study homogenization of a divergence form elliptic operator Aε of order 2m ≥ 4 with measurable ε-periodic coefficients, where ε is a small parameter. For the resolvent (Aε+1)−1, we construct an approximation with the remainder term of order ε2 in the operator (L2→Hm)-norm. To find approximations of such kind, we use the resolvent of the homogenized operator, solutions of several auxiliary problems on the unit cell of periodicity, and smoothing operators. The homogenized operator here differs from the one commonly employed in homogenization.