Fractional Sobolev spaces on Riemannian manifolds
type: Item
instance of: scholarly article
title: Fractional Sobolev spaces on Riemannian manifolds
author: Michele Caselli
author: Enric Florit-Simon
author: Joaquim Serra
published in: Mathematische Annalen
publication date: 2024-11-07T00:00:00Z
review text: Let \(M\) be a Riemannian manifold and \( s \in (0, 2) \). The paper studies three equivalent definitions for the fractional Hilbert space \( H^{s/2}(M) \) in terms of the heat kernel, a spectral decomposition, or an extension problem in a higher dimension. The precise singular behavior of the kernel associated with the fractional Hilbert norm is obtained. The authors also provide a monotonicity formula for stationary points of some fractional functionals (which includes the case of nonlocal \( s \)-minimal surfaces) and some estimates of independent interest for the extension problem.
reviewed by: Alberto Saldaña
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 35R01
zbMATH DE Number: 7940283
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Hilbert fractional norm
zbMATH Keywords: singular kernel
zbMATH Keywords: extension problem
MaRDI profile type: Publication
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DOI: 10.1007/S00208-024-02894-W
description: scientific article; zbMATH DE number 7940283