Pointwise estimates for the fundamental solutions of a class of singular parabolic problems

Abstract

We deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L∞ coefficients whose prototypes are the p-Laplacian (2N/(N + 1) < p < 2) and the porous medium equation (((N − 2)/N)+ < m < 1). We prove existence of and sharp pointwise estimates from above and from below for the fundamental solutions. Our results can be extended to general non-negative L1 initial data.