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 gradient’s norm. In particular, we show that our argument holds in the general framework of...

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Bibliographic Details
Published in:Bollettino della Unione matematica italiana (2008) 2024-06, Vol.17 (2), p.333-348
Main Authors: Ferrari, Fausto, Forcillo, Nicolò
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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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 gradient’s norm. In particular, we show that our argument holds in the general framework of Carnot groups.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-023-00393-5