Ragnedda, F. and Vernier Piro, S. and Vespri, V. (2012) Pointwise estimates for solutions of singular parabolic problems in R^N x [0;+∞). Technical Report 2012.02.17, no. 1, Dipartimento di Matematica "U.Dini", Universita' di Firenze.

Abstract

In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L1 coefficients, which prototypes are the p-laplacian ( 2N/(N+1) < p < 2) and the porous media equation ((N−2/N )_+ < m < 1). We prove pointwise estimates from above and from below assuming as initial data the Dirac mass. Our results can be extended to general nonnegative L1 initial data.