  We introduce Fundamental solutions of Barenblatt type for the equation
$u_t=\sum_{i=1}^N \bigg( |u_{x_i}|^{p_i-2}u_{x_i} \bigg)_{x_i}$, $p_i >2 \quad
\forall i=1,..,N$, on $\Sigma_T=\mathbb{R}^N \times[0,T]$, and we prove their
importance for the regularity properties of the solutions.
