Journal of Convex Analysis 15 (2008), No. 1, 017--037
Copyright Heldermann Verlag 2008
Optimal Shapes in Force Fields
Luca Granieri
Dip. di Matematica, Politecnico di Bari, via Orabona 4, 70125 Bari, Italy
l.granieri@poliba.it
Francesco Maddalena
Dip. di Matematica, Politecnico di Bari, via Orabona 4, 70125 Bari, Italy
f.maddalen@poliba.it
We study a variational problem involving material shapes, modeled as Radon measures on a given ambient space, in a force vector field. We prove some properties of absolutely continuity of the optimal shapes in dependence on the distributions of the zeros of the force field. More regularity properties of the optimal shapes, as well as simple geometrical characterizations, are established in the case of central force fields, in dependence on the regularity of the field and on the choice of the ambient space.
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