  In this paper we study the global boundedness for the solutions to a class of
possibly degenerate parabolic equations by De-Giorgi's iteration. As
applications, we show the existence of weak solutions for possibly degenerate
stochastic differential equations with singular diffusion and drift
coefficients. Moreover, by the Markov selection theorem of Krylov [8], we also
establish the existence of the associated strong Markov family.
