2022/08/31 by Gonzalo Galiano, Galiano, Gonzalo
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2208.14735
openalex publication_date 2022/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Talenti's type symmetrization properties for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable kernels is replacing the usual local diffusion defined by a second order differential operator. Using an approximation argument, we recover, as a corollary of our results, the classical Talenti's theorem. A novelty of our approach is that we replace the measure geometric tools employed in Talenti's proof by the use of the Riesz's rearrangement inequality, giving thus an alternative and somehow simpler proof than Talenti's one.