DEGENERATE PARABOLIC EQUATIONS WITH INITIAL DATA MEASURES

We address the problem oi existence of solutions to degenerate (and no ndegenerate) parabolic equations under optimal assumptions on the init ial data, which are assumed to be measures. The requirements imposed o n the initial data are connected both with the degeneracy of the princ ipal part of the equation. and with the form of the nonlinear forcing term; latter depends on the space gradient of a power of the solution. Applications to related problems are also outlined.