Abstract

Given a continuous function f ⁣:Sn−1→Rf\colon S^{n-1}\to\mathbb{R}, we consider the minimization of the functional ∫∂Af(νA) dHn−1\int_{\partial A} f(\nu_A)\,d\mathcal{H}^{n-1} with respect to the subset A of Rn\mathbb{R}^n, included in a class of convex bodies defined by surface or shape conditions. This corresponds to non-parametric formulations of older problems, including Newton's problem of the body of minimal resistance, following an approach due to G. Buttazzo and P. Guasoni [J. Convex Analysis 4 (1997) 343–351]. We establish existence and uniqueness results and some characterizations of the minimizers

Author information

Contact details are reproduced from the original publication and may be historical.

T. Lachand-Robert

Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique, 75252 Paris Cedex 05, France

lachand@ann.jussieu.fr

References

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Suggested citation

G. Carlier, T. Lachand-Robert. “Convex Bodies of Optimal Shape.” Journal of Convex Analysis 10 (2003), No. 1, 265–273. https://doi.org/10.68381/jca1015

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.