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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-1fe0ce2d-48f5-4b71-952e-2fa630c95c34

Czasopismo

Control and Cybernetics

Tytuł artykułu

On existence of shape optimization for a p-Laplacian equation over a class of open domains

Autorzy Guo, Bao-Zhu.  Yang, D. H. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In this paper, we introduce four new classes of open sets in general Euclidean space RN. It is shown that every such class of open sets is compact under the Hausdorff distance. The result is applied to a shape optimization problem of p-Laplacian equation. The existence of the optimal solution is presented.
Słowa kluczowe
EN Laplacian   shape optimization   existence  
Wydawca Systems Research Institute, Polish Academy of Sciences
Czasopismo Control and Cybernetics
Rocznik 2014
Tom Vol. 43, no. 1
Strony 15--31
Opis fizyczny Bibliogr. 22 poz.
Twórcy
autor Guo, Bao-Zhu.
  • Academy of Mathematics and Systems Science, Academia Sinica Beijing 100190, P.R.China
  • School of Computational and Applied Mathematics University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
autor Yang, D. H.
  • School of Mathematics, Central South University Changsha 410075, P.R.China, donghyang@139.com
Bibliografia
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7. Delfour, M.C. and Zol´esio, J.P. (2001) Shapes and Geometries. SIAM, New York.
8. Guo, B.Z. and Yang, D.H. (2012) Some compact classes of open sets under Hausdorff distance and application to shape optimization. SIAM J. Control Optim. 50 (1), 222-242.
9. Guo, B.Z. and Yang, D.H. (2013) On convergence of boundary Hausdorff measure and application to a boundary shape optimization problem. SIAM J. Control Optim. 51 (1), 253-272.
10. Hedberg, L.I. (1980) Spectral synthesis and stability in Sobolev spaces. In: Euclidean Harmonic Analysis. Lecture Notes in Math. 779, Springer-Verlag, Berlin, 73–103.
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18. Tiba, D. (2013) Finite element discretization in shape optimization problems for the stationary Navier-Stokes equation. System Modeling and Optimization. IFIP Advances in Information and Communication Technology. 391, 437-444.
19. Tiba, D. and Halanay, A. (2009) Shape optimization for stationary Navier- Stokes equations. Control Cybernet. 38 (4B), 1359-1374.
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