On locally concave functions on simplest non-convex domains

TL;DR

This paper proves that specific Bellman functions of multiple variables are the minimal locally concave functions on certain non-convex domains, extending previous results from two-variable cases.

Contribution

It generalizes earlier findings by establishing minimal local concavity of Bellman functions in higher dimensions on non-convex domains.

Findings

Bellman functions are minimal locally concave on certain domains

Extension of two-variable results to multiple variables

Generalization to non-convex domains

Abstract

We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about Bellman functions of two variables.