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

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