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Mathematics > Analysis of PDEs
Title: Nonlinear asymptotic mean value characterizations of holomorphic functions
(Submitted on 14 Jun 2023 (v1), last revised 7 May 2024 (this version, v2))
Abstract: 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.
Submission history
From: Riccardo Durastanti [view email][v1] Wed, 14 Jun 2023 11:17:10 GMT (24kb)
[v2] Tue, 7 May 2024 12:55:49 GMT (26kb)
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