An Introduction to Barenblatt Solutions for Anisotropic p-Laplace Equations

We introduce Fundamental solutions of Barenblatt type for the equation 1ut=∑i=1N(|uxi|pi−2uxi)xi,pi>2∀i=1,.,N,onΣT=ℝN×[0,T],$$displaystyle egin{aligned} u_t=sum _{i=1}^N igg (|u_{x_i}|{ }^{p_i-2}u_{x_i} igg )_{x_i}, quad quad p_i >2 quad orall i=1,.,N, quad quad ext{on} quad Sigma _T=mathbb {R}^N imes [0,T], end{aligned} $$ and we prove their importance for the regularity properties of the solutions.