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Obstacle problem for von Karman equations

Shing-Tung Yau Yang Gao

Optimization and Control mathscidoc:1912.43563

Advances in Applied Mathematics, 13, (2), 123-141, 1992.6
The free boundary value problem in obstacle problem for von Krmn equations is studied. By using the method of complementarity analysis, Rockafellar's theory of duality is generalized to the nonlinear variational problems and a complementarity theory of obstacle problem for von Krmn plates is established. We prove that the uniqueness and existence of solution directly depend on a complementary gap function. Moreover, a generalized dual extreme principle is established. We prove that the nonlinear primal variational inequality problem is eventually equivalent to a semi-quadratic dual optimization problem defined on a statically admissible space. This equivalence can be used to develop an effective numerical method for solving nonlinear free boundary value problems.
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@inproceedings{shing-tung1992obstacle,
  title={Obstacle problem for von Karman equations},
  author={Shing-Tung Yau, and Yang Gao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204052417411127},
  booktitle={Advances in Applied Mathematics},
  volume={13},
  number={2},
  pages={123-141},
  year={1992},
}
Shing-Tung Yau, and Yang Gao. Obstacle problem for von Karman equations. 1992. Vol. 13. In Advances in Applied Mathematics. pp.123-141. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204052417411127.
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