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

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

    Fausto Ferrari

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Nicolò Forcillo

Authors
  1. Fausto Ferrari
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  2. Nicolò Forcillo
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Correspondence to Nicolò Forcillo.

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Fausto Ferrari and Nicolò Forcillo are partially supported by INDAM-GNAMPA-2019 project: Proprietà di regolarità delle soluzioni viscose con applicazioni a problemi di frontiera libera.

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Ferrari, F., Forcillo, N. Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications. Boll Unione Mat Ital (2023). https://doi.org/10.1007/s40574-023-00393-5

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