Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups-Reference-Cited by-同舟云学术

Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups

Published:2024-07-29 Issue: Volume: Page:
ISSN:0373-3114
Container-title:Annali di Matematica Pura ed Applicata (1923 -)
language:en
Short-container-title:Annali di Matematica

Author:

Ferrari Fausto^ORCID,Giovagnoli Davide

Abstract

AbstractIn this paper we continue the analysis of an Alt–Caffarelli–Friedman (ACF) monotonicity formula in Carnot groups of step

$$s >1$$

s > 1 confirming the existence of counterexamples to the monotone increasing behavior. In particular, we provide a sufficient condition that implies the existence of some counterexamples to the monotone increasing behavior of the ACF formula in Carnot groups. The main tool is based on the lack of orthogonality of harmonic polynomials in Carnot groups. This paper generalizes the results proved in Ferrari and Forcillo (Atti Accad Naz Lincei Rend Lincei Mat Appl 34(2):295–306, 2023).

Funder

Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni

PRIN22

Alma Mater Studiorum - Università di Bologna

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s10231-024-01490-8.pdf

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