Comparison results for the fractional heat equation with a singular lower order term

Abstract

We provide symmetrization results in the form of mass concentration comparisons for fractional singular parabolic equations in infinite cylinders of the type $\Omega \times (0,T)$, where $\Omega \subset R^N$ ($N\ge 2$) is a bounded, open set with Lipschitz boundary, and $T>0$. The fundamental ingredients of the proof are an implicit time discretization procedure and a max/min argument, previously applied to nonlocal elliptic problems in the recent paper Brandolini et al. (2023).