Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 55, Issue 1, Pages 156-171Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1015844
Keywords
shape derivative; shape optimization; convex sets; support functions; gauge functions; Brunn-Minkowski
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Funding
- Laboratoire de Mathematiques Jean Leray
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We extend a formula for the computation of the shape derivative of an integral cost functional with respect to a class of convex domains, using the so-called support functions and gauge functions to express it. This is a priori a formula in shape optimization theory. However, the result also happens to be an extension of a well-known formula from the Brunn-Minkowski theory of convex bodies.
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