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

Abstract

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

23 pages