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

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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
Rocznik
Strony
15--31
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • 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
  • School of Mathematics, Central South University Changsha 410075, P.R.China
Bibliografia
  • 1. Adams, R.A. and Fournier, John J.F. (2003) Sobolev Spaces. Academic Press, Boston.
  • 2. Adams, D.R. and Hedberg, L.I. (1999) Function Spaces and Potential Theory. Springer, Berlin.
  • 3. Bucur, D. and Buttazzo, G. (2005) Variational Methods in Shape Optimization Problems. Birkhaeuser, Boston.
  • 4. Chenais, D. (1975) On the existence of a solution in a domain identification problem. J. Math. Anal. Appl. 52 (2), 189-219.
  • 5. Dinca, G., Jebelean, P. and Mawhin, J. (2001) Variational and topological methods for Dirichlet problems with p-Laplacian. Port. Math. 58 (3), 339-378.
  • 6. Delay, E. (2012) Smooth Compactly Supported Solutions of Some Undetermined Elliptic PDE with Gluing Applications. Comm. Partial Differential Equations. 37 (10), 1689-1716.
  • 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.
  • 11. Heinonen, J., Kilpelainen, T. and Martio, O. (2006) Nonlinear Potential Theory of Degenerate Elliptic Equation. Dover Publications, Mineola.
  • 12. He, Y. and Guo, B.Z. (2012) The existence of optimal solution for a shape optimization problem on starlike domain. J. Optim. Theory Appl. 152 (1), 21-30.
  • 13. Landkof, N.S. (1972) Foundations of Modern Potential Theory. Springer- Verlag, Berlin.
  • 14. Neittaanmaki, P., Sprekels, J. and Tiba, D. (2006) Optimization of Elliptic Systems: Theory and Applications. Springer-Verlag, New York.
  • 15. Pironneau, O. (1984) Optimal Shape Design for Elliptic Systems. Springer- Verlag, Berlin.
  • 16. Schneider, R. (1993) Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, London.
  • 17. Tiba, D (2003) A property of Sobolev spaces and existence in optimal design. Appl. Math. Optim. 47 (1), 45-58.
  • 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.
  • 20. Wang, G., Wang, L. and Yang, D.H. (2006) Shape Optimization of exterior domain stationary Navier-Stokes equations. SIAM. J. Control Optim. 45 (2), 532-547.
  • 21. Wang, G. and Yang, D.H. (2008) Decomposition of vector-valued divergence free Sobolev functions and shape optimization for stationary Navier- Stokes equations. Comm. Partial Differential Equations. 33 (1-3), 429- 449.
  • 22. Yang, D.H. (2009) Shape optimization of stationary Navier-Stokes equation over classes of convex domains. Nonlinear Anal. 71 (12), 6202-6211.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1fe0ce2d-48f5-4b71-952e-2fa630c95c34
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