arXiv subjects
Publications and source records attributed to Filippo Maria Cassanello.
We establish an integral Harnack inequality and expansion of positivity for nonnegative weak solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.
We prove local Hölder continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations $\partial_t (u_q) - \text{div} (|Du|^{p-2} Du) = 0$ for $p > 2$, $ 0 < q < p-1$. The proof relies on expansion of positivity results combined with the study of an alternative (related to DeGiorgi-type lemmas) and an exponential shift which allows us to deal with the intrinsic geometry associated to the problem.