Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications

In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Ferrari, Fausto, cillo, Nicolò
Format: Article
Language:English
Subjects:
Lie groups
Online Access:Get full text
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Summary:In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework of Carnot groups.
ISSN:2331-8422
DOI:10.48550/arxiv.2310.13264