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.
Author: | Kevin Sturm |
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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 |