Lagrange method in shape optimization for a class of non-linear partial differential equations: A material derivative free approach

Please always quote using this URN:urn:nbn:de:0296-matheon-12977
  • In this paper a new theorem is formulated which allows a rigorous proof of the shape differentiability without the usage of the material derivative; the domain expression is automatically obtained and the boundary expression is easy to derive. Furthermore, the theorem is applied to a cost function which depends on a quasi-linear transmission problem. Using a Gagliardo penalization the existence of optimal shapes is established.

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Metadaten
Author:Kevin Sturm
URN:urn:nbn:de:0296-matheon-12977
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/05/20
Release Date:2014/05/20
Tag:Lagrange method, shape derivative, non-linear PDE, material derivative
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Qxx Manifolds [See also 58Exx] / 49Q10 Optimization of shapes other than minimal surfaces [See also 90C90]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Qxx Manifolds [See also 58Exx] / 49Q12 Sensitivity analysis
Preprint Number:1064
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