Calculus of Variations and Geometric Measure Theory
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L. Granieri - F. Maddalena

Optimal shapes in force fields

created by granieri on 11 Apr 2006
modified on 06 Sep 2010


Published Paper

Inserted: 11 apr 2006
Last Updated: 6 sep 2010

Journal: J. Convex Analysis
Volume: 15
Number: 17-37
Year: 2008

The original paper is available on http:/www.heldermann.deJCAJCA15jca15.htm


\begin{abstract}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.\end{abstract}


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