6 research outputs found
Estimates in homogenization of degenerate elliptic equations by spectral method
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