CONVEX AND QUASICONVEX FUNCTIONS IN METRIC GRAPHS

被引：1

作者：

Del Pezzo, Leandro M. ^{[1
,2
]}

Frevenza, Nicolas ^{[3
]}

Rossi, Julio D. ^{[1
,2
]}

机构：

[1] Univ Buenos Aires, CONICET, Pabellon 1,Ciudad Univ, Buenos Aires 1428, DF, Argentina

[2] Univ Buenos Aires, FCEyN, Dept Matemat, Pabellon 1,Ciudad Univ, Buenos Aires 1428, DF, Argentina

[3] Univ Republica, FCEA, Dept Metodos Mateat & Cuantitativos, Gonzalo Ramrez 1926, Montevideo 11200, Uruguay

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2021年 / 16卷 / 04期

关键词：

Convexity; quasiconvexity; metric graph; convex envelope; quasiconvex envelope; PARTIAL-DIFFERENTIAL-EQUATIONS; ENVELOPE; GAMES;

D O I：

10.3934/nhm.2021019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, u '' = 0 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.

引用

页码：591 / 607

页数：17

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