Bäuerlein: Weak Harnack inequality for doubly non-linear equations of slow diffusion type

Date: 2024-05-22

Time: 14:00 - 14:30

Zoom link: https://kva-se.zoom.us/j/9217561880


Fabian Bäuerlein, University of Salzburg


In this talk we consider doubly non-linear equations, whose prototype equation is given by

\begin{equation*} \partial_t \big(|u|^{q-1} u \big) – \mathrm{div} \big( |Du|^{p-2} Du \big) = 0 \end{equation*} for parameters \(q,p\) that satisfy \(q>0\) as well as \(p>1\). More precisely, the vector field of the divergence term satisfies standard assumptions for \(p\)-growth. We establish a weak Harnack inequality for non-negative weak super-solutions in the entire slow diffusion regime, where the latter is characterized by the inequality \(p-q-1>0\) for the parameters.