Journal Article

Shapes and measures


in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 16, issue 3, pages 207-220
Published in print September 1999 | ISSN: 0265-0754
Published online September 1999 | e-ISSN: 1471-6887 | DOI:
Shapes and measures

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It is a well-known fact that a measurable set a shape can be considered as a measure; the aim of this work is to solve an optimal-shape problem in such a way that it also answers the question of whether measures can be considered as shapes. This paper introduces a new method for solving problems of optimal shape design; by a process of embedding, the problem is replaced by another in which we seek to minimize a linear form over a subset of the product of two measure spaces defined by linear equalities. This minimization is global, and the theory allows us to develop a computational method which enables us to find the solution by finite-dimensional linear programming. The nearly optimal pair (C, dC) is obtained via the optimal pair of measures by an approximation procedure. It is sometimes necessary to apply a standard minimization algorithm, because of some limitations in the accuracy. Some examples are presented.

Journal Article.  0 words. 

Subjects: Mathematics

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