Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 46 | |
Number of page(s) | 29 | |
DOI | https://doi.org/10.1051/cocv/2024034 | |
Published online | 04 June 2024 |
Nonlinear asymptotic mean value characterizations of holomorphic functions
1
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, via Cintia, Monte S. Angelo, 80126 Napoli, Italy
2
Dipartimento di Matematica ed Informatica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy
* Corresponding author: riccardo.durastanti@unina.it
Received:
14
June
2023
Accepted:
9
April
2024
Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the classical Cauchy-Riemann equations. From these asymptotic characterizations, we derive suitable asymptotic mean value properties, which are used to construct appropriate vectorial dynamical programming principles. The aim is to construct approximation schemes for the so-called contact solutions, recently introduced by N. Katzourakis, of the nonlinear systems here considered.
Mathematics Subject Classification: 35J60 / 35J46 / 35J47 / 30A10 / 30C62 / 35K55
Key words: Holomorphic functions / quasiregular maps / mean value property / asymptotic mean value property for nonlinear systems / contact solutions
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.