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Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIShape Differentiability of Lagrangians and Application to Overdetermined Problems

Mathematical Analysis of Continuum Mechanics and Industrial Applications III: Shape... [A class of geometry-dependent Lagrangians is investigated in a functional analysis framework with respect to the property of shape differentiability. General results are presented due to Delfour–Zolésio who adopted to shape optimization an abstract theorem of Correa–Seeger on the directional differentiability. A crucial point concerns the bijective property of function spaces as well as their feasible sets that must be preserved under a kinematic flow of geometry. The shape differentiability result is applied to overdetermined free-boundary and inverse problems expressed by least-square solutions. The theory is supported by explicit formulas obtained for calculation of the shape derivative.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIShape Differentiability of Lagrangians and Application to Overdetermined Problems

Part of the Mathematics for Industry Book Series (volume 34)
Editors: Itou, Hiromichi; Hirano, Shiro; Kimura, Masato; Kovtunenko, Victor A.; Khludnev, Alexandr M.
Kovtunenko, Victor A.; Ohtsuka, Kohji
Mathematical Analysis of Continuum Mechanics and Industrial Applications III — Aug 30, 2020
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Publisher
Springer Singapore
Copyright
© Springer Nature Singapore Pte Ltd. 2020
ISBN
978-981-15-6061-3
Pages
97 –110
DOI
10.1007/978-981-15-6062-0_7
Publisher site
See Chapter on Publisher Site

Abstract

[A class of geometry-dependent Lagrangians is investigated in a functional analysis framework with respect to the property of shape differentiability. General results are presented due to Delfour–Zolésio who adopted to shape optimization an abstract theorem of Correa–Seeger on the directional differentiability. A crucial point concerns the bijective property of function spaces as well as their feasible sets that must be preserved under a kinematic flow of geometry. The shape differentiability result is applied to overdetermined free-boundary and inverse problems expressed by least-square solutions. The theory is supported by explicit formulas obtained for calculation of the shape derivative.]

Published: Aug 30, 2020

Keywords: Shape derivative; Lagrangian; Correa–Seeger theorem; Delfour–Zolésio theorem; State-constrained shape optimization; Free-boundary; Inverse problem

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