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Optimal Shapes for Tree Roots

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 نشر من قبل Sondre Tesdal Galtung
 تاريخ النشر 2021
  مجال البحث
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The paper studies a class of variational problems, modeling optimal shapes for tree roots. Given a measure $mu$ describing the distribution of root hair cells, we seek to maximize a harvest functional $mathcal{H}$, computing the total amount of water and nutrients gathered by the roots, subject to a cost for transporting these nutrients from the roots to the trunk. Earlier papers had established the existence of an optimal measure, and a priori bounds. Here we derive necessary conditions for optimality. Moreover, in space dimension $d=2$, we prove that the support of an optimal measure is nowhere dense.



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