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× (0,T), where omegaCRN (N ≥ 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).