A new glance to the Alt-Caffarelli-Friedman monotonicity formula

Fausto Ferrari; Nicolò Forcillo; Fausto Ferrari; Nicolò Forcillo

doi:10.3934/mine.2020030

Mathematics in Engineering

2020, Volume 2, Issue 4: 657-679. doi: 10.3934/mine.2020030

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A new glance to the Alt-Caffarelli-Friedman monotonicity formula

Fausto Ferrari ^,,
Nicolò Forcillo

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

Received: 25 November 2019 Accepted: 16 March 2020 Published: 26 May 2020

In this paper we revisit the proof of the Alt-Caffarelli-Friedman monotonicity formula. Then, in the framework of the Heisenberg group, we discuss the existence of an analogous monotonicity formula introducing a necessary condition for its existence, recently proved in [18].
- monotonicity formulas,
- Heisenberg group,
- free boundary problems,
- two-phase problems
Citation: Fausto Ferrari, Nicolò Forcillo. A new glance to the Alt-Caffarelli-Friedman monotonicity formula[J]. Mathematics in Engineering, 2020, 2(4): 657-679. doi: 10.3934/mine.2020030

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Abstract

In this paper we revisit the proof of the Alt-Caffarelli-Friedman monotonicity formula. Then, in the framework of the Heisenberg group, we discuss the existence of an analogous monotonicity formula introducing a necessary condition for its existence, recently proved in [18].

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