Generalized Local Maximum Principles for Finite-Difference Operators
نویسنده
چکیده
The generalized local maximum principle for a difference operator L» asserts that if Lam(jc) > 0 then Vu cannot attain its positive maximum at the net-point x. Here r is a local net-operator such that Tu = u + 0(/i) for any smooth function u. This principle, with simple forms of V, is proved for some quite general classes of second-order elliptic operators Lh, whose associated global matrices are not necessarily monotone. It is shown that these generalized principles can be used for easy derivation of global a priori estimates to the solutions of elliptic difference equations and to their difference-quotients. Some examples of parabolic difference equations are also treated.
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