Shari Moskow
University of Florida
Abstract: One important class of functions in homogenization theory are solutions to elliptic equations which have both oscillating coefficients and boundary data. These boundary correctors are used to obtain o(epsilon) approximations for the standard elliptic periodic homogenization problem (where epsilon is the size of the period cell), and their limits are also needed to obtain first order corrections to the eigenvalues of a periodic medium. The effective values of these corrector functions also play a role in the convergence rates of Multiscale Finite Element Methods. Unfortunately, when one has both oscillating coefficients and boundary data, the effective equations are not known except in certain cases. Even in these special cases the answer is not what one would expect. Careful analysis revealed that the effective equation may not be unique. In addition, the effective boundary values are not the weak limits one would expect. They depend on a boundary layer function on a half space.