Existence and Uniqueness results of Some Nonlinear Parabolic Equations with Uniformly Continuous Data

In this note, we consider the Cauchy problem of nonlinear degenerate parabolic equations including the level set equation of the mean curvatue equation and the p-Laplace diffusion equation with p ≥ 2. We shall give existence and uniqueness results to such equations provided that the initial data is uniformly continuous.