A note on contact shape optimization with semicoercive state problems

Jaroslav Haslinger

Applications of Mathematics (2002)

  • Volume: 47, Issue: 5, page 397-410
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Haslinger, Jaroslav. "A note on contact shape optimization with semicoercive state problems." Applications of Mathematics 47.5 (2002): 397-410. <http://eudml.org/doc/33122>.

@article{Haslinger2002,
abstract = {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.},
author = {Haslinger, Jaroslav},
journal = {Applications of Mathematics},
keywords = {shape optimization; semicoercive problems; shape optimization; semicoercive problems},
language = {eng},
number = {5},
pages = {397-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on contact shape optimization with semicoercive state problems},
url = {http://eudml.org/doc/33122},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Haslinger, Jaroslav
TI - A note on contact shape optimization with semicoercive state problems
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 5
SP - 397
EP - 410
AB - 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.
LA - eng
KW - shape optimization; semicoercive problems; shape optimization; semicoercive problems
UR - http://eudml.org/doc/33122
ER -

References

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  7. 10.1007/BF00249518, Arch. Rational Mech. Anal. 36 (1970), 305–334. (1970) MR0252844DOI10.1007/BF00249518
  8. Hausdorff convergence of domains and their boundaries in shape optimal design, Control Cybernet. 30 (2001), 23–44. (2001) 
  9. 10.1051/m2an/1981150302371, RAIRO Anal. Numer. 15 (1981), 237–248. (1981) Zbl0467.35019MR0631678DOI10.1051/m2an/1981150302371
  10. Optimal Shape Design for Elliptic Systems. Springer Series in Computational Physics, Springer-Verlag, New York, 1984. (1984) MR0725856
  11. Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer-Verlag, Berlin, 1992. (1992) MR1215733

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