| Title:
|
A note on contact shape optimization with semicoercive state problems (English) |
| Author:
|
Haslinger, Jaroslav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2002 |
| Pages:
|
397-410 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note deals with contact shape optimization for problems involving “floating” structures. The boundedness of solutions to state problems with respect to admissible domains, which is the basic step in the existence analysis, is a consequence of Korn’s inequality in coercive cases. In semicoercive cases (meaning that floating bodies are admitted), the Korn inequality cannot be directly applied and one has to proceed in another way: to use a decomposition of kinematically admissible functions and a Korn type inequality on appropriate subspaces. In addition, one has to show that the constant appearing in this inequality is independent with respect to a family of admissible domains. (English) |
| Keyword:
|
shape optimization |
| Keyword:
|
semicoercive problems |
| MSC:
|
49A29 |
| MSC:
|
65K10 |
| MSC:
|
73K25 |
| idZBL:
|
Zbl 1090.65517 |
| idMR:
|
MR1924677 |
| DOI:
|
10.1023/A:1021709907750 |
| . |
| Date available:
|
2009-09-22T18:10:58Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134504 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] L. Holzleitner: Hausdorff convergence of domains and their boundaries in shape optimal design.Control Cybernet. 30 (2001), 23–44. |
| Reference:
|
[9] J. A. Nitsche: On Korn’s second inequality.RAIRO Anal. Numer. 15 (1981), 237–248. Zbl 0467.35019, MR 0631678, 10.1051/m2an/1981150302371 |
| Reference:
|
[10] O. Pironneau: Optimal Shape Design for Elliptic Systems. Springer Series in Computational Physics.Springer-Verlag, New York, 1984. MR 0725856 |
| Reference:
|
[11] J. Sokolowski, J. P. Zolesio: Introduction to Shape Optimization: Shape Sensitivity Analysis.Springer-Verlag, Berlin, 1992. MR 1215733 |
| . |
