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
收藏
页码：591 / 607
页数：17
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