科研之友
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摘要
A periodic differential operator of the form A(epsilon) = (D(P))*g(x/epsilon)D(P) is considered on L(2)(R(d)); here g(x) is a positive definite symmetric tensor of order 2p periodic with respect to a lattice Gamma. The behavior of the resolvent of the operator A(epsilon) as epsilon -> 0 is studied. It is shown that the resolvent (A(epsilon) + I)(-1) converges in the operator norm to the resolvent of the effective operator A(0) with constant coefficients. For the norm of the difference of resolvents, an estimate of order epsilon is obtained.
- 出版日期2011-10
