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

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

This contribution is part of the Special Issue: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday
Guest Editor: Gianmaria Verzini
Link: https://www.aimspress.com/newsinfo/1429.html

Special Issues: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday

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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Keywords 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. Mathematics in Engineering, 2020, 2(4): 657-679. doi: 10.3934/mine.2020030

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