The Limit Absorption Principle and Homogenization Procedure for Periodic Elliptic Operators

摘要

For a periodic matrix elliptic operator A(epsilon) with (x/epsilon-dependent) rapidly oscillating coefficients, a certain analog of the limit absorption principle is proved. It is shown that the bordered resolvent < x >(-/2-delta)(A(epsilon) - (eta +/- i epsilon(sigma))I)(-1/2-delta) has a limit in the operator norm in L-2 as epsilon -> 0 provided that eta > 0, delta > 0, and 0 < sigma < 1/2.