论文标题
凸和Quasiconvex在度量图中的函数
Convex and quasiconvex functions in metric graphs
论文作者
论文摘要
我们在度量图上研究凸和准胶函数。给定度量图中的一组点，我们考虑了规定基准的下方最大的凸功能。我们将此最大的凸功能表征为简单微分方程的独特最大粘度订阅，边缘上的$ u''= 0 $，以及顶点处的非线性传输条件。我们还研究了准分子函数的类似问题，并获得了低于给定基准的最大准胶函数的表征。
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.
