On a Shape Derivative Formula in the Brunn--Minkowski Theory | Zendy

A. Boulkhemair | Zendy

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On a Shape Derivative Formula in the Brunn--Minkowski Theory

Author(s) -

A. Boulkhemair

Publication year - 2017

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/15m1015844

Subject(s) - mathematics , minkowski space , regular polygon , mathematical analysis , convex analysis , convex body , convex conjugate , mixed volume , pure mathematics , convex optimization , geometry

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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