Open AccessConvex and quasiconvex functions in metric graphs
Author(s) -
Leandro M. Del Pezzo,
Nicolás Frevenza,
Julio D. Rossi
Publication year - 2021
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2021019
Subject(s) - quasiconvex function , mathematics , convex function , combinatorics , regular polygon , graph , convex set , function (biology) , pseudoconvex function , mathematical analysis , discrete mathematics , pure mathematics , convex optimization , geometry , evolutionary biology , biology
We study convex and quasiconvex functions on a metric graph. Given a set of points in the metric graph, we consider the largest convex function below the prescribed datum. We characterize this largest convex function as the unique largest viscosity subsolution to a simple differential equation, \begin{document}$ u'' = 0 $\end{document} on the edges, plus nonlinear transmission conditions at the vertices. We also study the analogous problem for quasiconvex functions and obtain a characterization of the largest quasiconvex function that is below a given datum.