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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 765020, 12 pages
http://dx.doi.org/10.1155/2013/765020
Research Article

On the Dirichlet Problem for the Stokes System in Multiply Connected Domains

Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy

Received 24 April 2012; Accepted 28 November 2012

Academic Editor: Chun-Lei Tang

Copyright © 2013 Alberto Cialdea et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Cattabriga, “Su un problema al contorno relativo al sistema di equazioni di Stokes,” Rendiconti del Seminario Matematico della Università di Padova, vol. 31, pp. 308–340, 1961. View at Zentralblatt MATH
  2. V. A. Solonnikov, “On estimates of Green's tensors for certain boundary problems,” Doklady Akademii Nauk, vol. 130, pp. 988–991, 1960 (Russian), Translates in Soviet Mathematics Doklady, vol. 1, pp. 128–131, 1960. View at Zentralblatt MATH
  3. M. Kohr, “A mixed boundary value problem for the unsteady Stokes system in a bounded domain in ℝn,” Engineering Analysis with Boundary Elements, vol. 29, no. 10, pp. 936–943, 2005. View at Publisher · View at Google Scholar
  4. M. Kohr, “The Dirichlet problems for the Stokes resolvent equations in bounded and exterior domains in n,” Mathematische Nachrichten, vol. 280, no. 5-6, pp. 534–559, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. M. Kohr, “The interior Neumann problem for the Stokes resolvent system in a bounded domain in n,” Archives of Mechanics, vol. 59, no. 3, pp. 283–304, 2007. View at Zentralblatt MATH
  6. M. Kohr, “Boundary value problems for a compressible Stokes system in bounded domains in n,” Journal of Computational and Applied Mathematics, vol. 201, no. 1, pp. 128–145, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. P. Maremonti, R. Russo, and G. Starita, “On the Stokes equations: the boundary value problem,” in Advances in Fluid Dynamics, pp. 69–140, Quaderni di Matematica Aracne, Rome, Italy, 1999. View at Zentralblatt MATH
  8. G. Starita and A. Tartaglione, “On the traction problem for the Stokes system,” Mathematical Models & Methods in Applied Sciences, vol. 12, no. 6, pp. 813–834, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. A. Cialdea, “On the oblique derivation problem for the Laplace equation, and related topics,” Rendiconti della Accademia Nazionale delle Scienze detta dei XL, vol. 12, no. 1, pp. 181–200, 1988.
  10. G. Fichera, “Una introduzione alla teoria delle equazioni integrali singolari,” Rendiconti di Matematica, vol. 17, pp. 82–191, 1958. View at Zentralblatt MATH
  11. S. G. Mikhlin and S. Prössdorf, Singular Integral Operators, Springer, Berlin, Germany, 1986.
  12. A. Cialdea and G. C. Hsiao, “Regularization for some boundary integral equations of the first kind in mechanics,” Rendiconti della Accademia Nazionale delle Scienze detta dei XL, vol. 19, pp. 25–42, 1995. View at Zentralblatt MATH
  13. A. Cialdea, V. Leonessa, and A. Malaspina, “On the Dirichlet and the Neumann problems for Laplace equation in multiply connected domains,” Complex Variables and Elliptic Equations, vol. 57, no. 10, pp. 1035–1054, 2012. View at Publisher · View at Google Scholar
  14. A. Malaspina, “Regularization for integral equations of the first kind in the theory of thermoelastic pseudo-oscillations,” Applied Mathematics, Informatics and Mechanics, vol. 9, no. 2, pp. 29–51, 2004.
  15. A. Malaspina, “On the traction problem in mechanics,” Archives of Mechanics, vol. 57, no. 6, pp. 479–491, 2005. View at Zentralblatt MATH
  16. A. Cialdea, V. Leonessa, and A. Malaspina, “Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains,” Boundary Value Problems, vol. 2011, aticle 53, 2011. View at Publisher · View at Google Scholar
  17. A. Malaspina, “Regularization of some integral equations of the first kind,” AIP Conference Proceedings, vol. 1281, pp. 916–919, 2010. View at Publisher · View at Google Scholar
  18. A. Malaspina, “Integral representation for the solution of Dirichlet problem for the stokes system,” AIP Conference Proceedings, vol. 1389, pp. 473–476, 2011. View at Publisher · View at Google Scholar
  19. A. Cialdea, E. Dolce, A. Malaspina, and V. Nanni, “On an integral equation of the first kind arising in the theory of Cosserat,” submitted.
  20. A. Cialdea, “A general theory of hypersurface potentials,” Annali di Matematica Pura ed Applicata, vol. 168, pp. 37–61, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. V. D. Kupradze, T. G. Gegelia, M. O. Basheleĭshvili, and T. V. Burchuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, vol. 25 of North-Holland Series in Applied Mathematics and Mechanics, North-Holland Publishing, Amsterdam, The Netherlands, 1979.
  22. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Science Publishers, New York, NY, USA, 1969.
  23. W. V. D. Hodge, “A dirichlet problem for harmonic functionals, with applications to analytic varities,” Proceedings of the London Mathematical Society, vol. S2-36, no. 1, pp. 257–303, 1934. View at Publisher · View at Google Scholar
  24. A. Cialdea, “On the finiteness of the energy integral in elastostatics with non-absolutely continuous data,” Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei IX, vol. 4, no. 1, pp. 35–42, 1993. View at Zentralblatt MATH
  25. A. Cialdea, “The multiple layer potential for the biharmonic equation in n variables,” Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei IX, vol. 3, no. 4, pp. 241–259, 1992. View at Zentralblatt MATH