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 𝛺× (0,𝑇), where 𝛺⊂R𝑁 (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).