S. Moskow
University of Florida
Boundary Correctors for Periodic Media
Shari Moskow*
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 
approximations for
the standard elliptic periodic homogenization problem (where
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.
*This is joint work with Michael Vogelius and Eric Bonnetier
