A Talenti-type comparison theorem for the \(p\)-Laplacian on \(\operatorname{RCD}(K,N)\) spaces and some applications. (English) Zbl 07919116
Summary: In this paper, we prove a Talenti-type comparison theorem for the \(p\)-Laplacian with Dirichlet boundary conditions on open subsets of a normalized \(\operatorname{RCD}(K,N)\) space with \(K>0\) and \(N\in(1,\infty)\). 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.
MSC:
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
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