Consider the nonlinear degenerate parabolic equation
where subscripts denote partial differentiation. The functions a and b are hypothesized to belong to and be such that for , and and are locally Hölder continuous on (0, and and . In the present paper the author has established improved existence and uniqueness theorems for the Cauchy problem, the Cauchy-Dirichlet problem, and the first boundary value problem for equation (1). The comparison principles for generalized solutions of equation (1) and the relationship between the results given in this paper and those in earlier publications is also given.