The goal of the paper is to prove an exact representation formula for the Laplacian of the distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of metric measure spaces satisfying Ricci curvature lower bounds in a synthetic sense (more precisely in essentially nonbranching MCP.K; N/-spaces). Such a representation formula makes apparent the classical upper bounds together with lower bounds and a precise description of the singular part. The exact representation formula for the Laplacian of a general 1-Lipschitz function holds also (and seems new) in a general complete Riemannian manifold.

New formulas for the Laplacian of distance functions and applications / Cavalletti, F.; Mondino, A.. - In: ANALYSIS & PDE. - ISSN 2157-5045. - 13:7(2020), pp. 2091-2148. [10.2140/apde.2020.13.2091]

New formulas for the Laplacian of distance functions and applications

Cavalletti, F.
;
2020-01-01

Abstract

The goal of the paper is to prove an exact representation formula for the Laplacian of the distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of metric measure spaces satisfying Ricci curvature lower bounds in a synthetic sense (more precisely in essentially nonbranching MCP.K; N/-spaces). Such a representation formula makes apparent the classical upper bounds together with lower bounds and a precise description of the singular part. The exact representation formula for the Laplacian of a general 1-Lipschitz function holds also (and seems new) in a general complete Riemannian manifold.
13
7
2091
2148
https://arxiv.org/abs/1803.09687
Cavalletti, F.; Mondino, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/126749
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