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arXiv · 2011.14718

Convex and quasiconvex functions in metric graphs

Leandro M. Del Pezzo·Nicolás Frevenza·Julio D. Rossi
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Abstract

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.

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Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi. 2020-11-30. Convex and quasiconvex functions in metric graphs. https://arxiv.org/abs/2011.14718

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