Parabolic De Giorgi Class With Variable Exponent P(x) And Holder Continuity

We introduce the Parabolic De Giorgi class Bp(x)(ΩT,M,γ,δ). With the help of De Giorgi and Moser iteration.Holder continuity of a function in the Parabolic De Giorgi class is established. As an application:the Holder continuity of weak solutions of quasi-linear degenerate parabolie equations with nonstandard p(x)-growth is proved.