A Talenti-type comparison theorem for the p-Laplacian on RCD(K,N) spaces and some applications

2024/01/21 by Wu, Wenjing · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2401.11456

Abstract

In this paper, we prove a Talenti-type comparison theorem for the p-Laplacian with Dirichlet boundary conditions on open subsets of a RCD(K,N) space with K>0 and N∈ (1,∞). The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov-Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the p-Laplacian and a related quantitative stability result.

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