Partial differential equations--a Harnack's inequality and holder continuity for solutions of mixed type evolution equations

We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is [mu](x) [partial derivative]u / [partial derivative]t - [DELTA]u = 0 where [mu] can be positive, null and negative, so that elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local bounded-ness and show a Harnack inequality which, as by-products, gives Holder-continuity, in particular in the interface I where [mu] change sign, and a maximum principle. Key words: Mixed type equations, Harnack's inequality, Holder-continuity MATHEMATICS SUBJECT CLASSIFICATION: 35M10, 35B65