Alberto Bressan, Sondre T. Galtung
Published 2020-06-02Version 1
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.
Comments: 23 pages, 10 figures
Approximation of shape optimization problems with non-smooth PDE constraints
A shape optimization problem on planar sets with prescribed topology
A duality principle and related numerical method for a class of shape optimization problems in elasticity
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