Eurica Henriques
Centro de Matemática, Polo CMAT-UTAD
In this talk we presente our contribution to the understanding of the right form of Harnack inequalities for singular parabolic equations. Namely, we show that an intrinsic weak form of Harnack estimates holds for doubly nonlinear equations whose prototype is $$u_t-\textrm{div}\big(|u|^{m-1} |Du|^{p-2} Du\big)=0 , \qquad p>1,$$ in the case $m+p=2$ and $p>1$.
This was a joint work with S. Fornaro (Univ. Pavia) and Vincenzo Vespri (Univ. Florence).