An Introduction to Barenblatt Solutions for Anisotropic $p$-Laplace Equations

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.