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).
Barbara Brandolini, Ida De Bonis, Vincenzo Ferone, Bruno Volzone (2025). Comparison results for the fractional heat equation with a singular lower order term. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 87 [10.1016/j.nonrwa.2025.104434].
Comparison results for the fractional heat equation with a singular lower order term
Barbara Brandolini;
2025-06-27
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).
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