Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients
Tatiana Aleksandrovna Suslina · Complex Variables and Elliptic Equations · 2017
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 on and .