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.
Ferrari F., Forcillo N. (2023). Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 17(2), 333-348 [10.1007/s40574-023-00393-5].
Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications
Ferrari F.;
2023
Abstract
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.File in questo prodotto:
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