paper

On a Shape Optimization Problem for Tree Branches

arXiv:2006.01679 · doi:10.3934/nhm.2020031

Abstract

This paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of the trunk to all the leaves. In the case of 2 space dimensions, the solution is proved to be unique, and explicitly determined.

23 pages, 10 figures