| Abstract: | In this paper the author discusses the quasilinear parabolic equation$$[frac{{partial u}}{{partial t}} = frac{partial }{{partial {x_i}}}[{a_{ij}}(x,t,u)frac{{partial u}}{{partial {x_j}}}] + {b_i}(x,t,u)frac{{partial u}}{{partial {x_i}}} + c(x,t,u)]$$Which is uniformly degenerate at $[u = 0]$. Let $[u(x,t)]$ be a classical solution of the equation satisfying $[0 < u(x,t) le M]$. Under some assumptions the author establishes the interior estimations of Holdercoefficient of the solution for the equation and the global estimations for Cauchy problems and the first boundary value problems, where Holder ooeffioients and exponents are independent of the lower positive bound of $[u(x,t)]$. |
