Abstract
A divergent-type elliptic operator of arbitrary even order 2m is studied. Coefficients of the operator are
-periodic,
is a small parameter. The resolvent equation
is solvable in the Sobolev space
of order m for any
, provided the parameter
is sufficiently large,
, where the bound
depends only on constants from ellipticity condition. The limit equation is of the same type but with constant coefficients, that is,
. The limit operator
can be considered here, for instance, in the sense of G-convergence. We prove that the resolvent
approximates
in operator
-norm with the estimate
, as
. We find also the approximation of the resolvent
in operator
-norm. This is the sum
, where
is a correcting operator whose structure is given. We prove the estimate
, as
.
Notes
No potential conflict of interest was reported by the author.