Estimates in homogenization of degenerate elliptic equations by spectral method

Abstract

We study the homogenization of elliptic equations stated in L²-space with degenerate weight. Both coefficients of the differential operator and the weight are ε-periodic and highly oscillating as ε tends to zero. Under minimal hypotheses on the coefficients and the weight we prove estimates of order ε and ε² for L²-norm of the difference between the exact solution and its appropriate approximations by L²-norm of the right-side function. The spectral method based on Bloch decomposition is used. In the case of nonunique solution provided that the weight is not regular we consider estimates for any of so-called variational solutions.