Calculus of Variations and Geometric Measure Theory

R. Durastanti - R. Magnanini

Nonlinear asymptotic mean value characterizations of holomorphic functions

created by durastanti on 07 Nov 2023
modified on 04 Jun 2024


Published Paper

Inserted: 7 nov 2023
Last Updated: 4 jun 2024

Journal: ESAIM: Control, Optimisation and Calculus of Variations
Volume: 30
Number: 46
Year: 2024
Doi: 10.1051/cocv/2024034


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.