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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 302628, 4 pages
The Dirichlet Problem for the Equation in the Exterior of Nonclosed Lipschitz Surfaces
KIAM, Miusskaya Sq. 4, Moscow 125047, Russia
Received 20 March 2012; Accepted 7 September 2012
Academic Editor: Attila Gilányi
Copyright © 2013 P. A. Krutitskii. 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.
- W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, UK, 2000.
- G. Verchota, “Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains,” Journal of Functional Analysis, vol. 59, no. 3, pp. 572–611, 1984.
- D. S. Jerison and C. E. Kenig, “The Neumann problem on Lipschitz domains,” American Mathematical Society Bulletin, vol. 4, no. 2, pp. 203–207, 1981.
- P. Grisvard, Boundary Value Problems in Nonsmooth Domains, Pitman, London, UK, 1985.
- B. E. J. Dahlberg, “On the Poisson integral for Lipschitz and -domains,” Studia Mathematica, vol. 66, no. 1, pp. 13–24, 1979.
- C. Sbordone and G. Zecca, “The -solvability of the Dirichlet problem for planar elliptic equations, sharp results,” The Journal of Fourier Analysis and Applications, vol. 15, no. 6, pp. 871–903, 2009.
- I. K. Lifanov, L. N. Poltavskii, and G. M. Vainikko, Hypersingular Integral Equations and Their Applications, CRC Press, Boca Raton, Fla, USA, 2004.
- A.Ya. Povzner and I. V. Sukharevskii, “Integral equations of second kindin a problem of diffraction by an infinitely thin screen,” Soviet Physics Doklady, vol. 4, pp. 798–802, 1960.
- P. E. Berkhin, “Problem of diffraction at a fine screen,” Siberian Mathematical Journal, vol. 25, no. 1, pp. 31–42, 1984.
- P. A. Krutitskii, “The Dirichlet problem for the 2D laplace equation in a domain with cracks without compatibility conditions at tips of the cracks,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 269607, 20 pages, 2012.
- P. A. Krutitskii, “The Dirichlet problem for the 2-dimensional Laplace equation in a multiply connected domain with cuts,” Proceedings of the Edinburgh Mathematical Society, vol. 43, no. 2, pp. 325–341, 2000.
- P. A. Krutitskii, “The 2-dimensional Dirichlet problem in an external domain with cuts,” Zeitschrift für Analysis und ihre Anwendungen, vol. 17, no. 2, pp. 361–378, 1998.
- P. A. Krutitskii, “The Dirichlet problem for the 2-D Helmholtz equation in a multiply connected domain with cuts,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 77, no. 12, pp. 883–890, 1997.
- P. A. Krutitskii, “The 2D Dirichlet problem for the propagative Helmholtz equation in an exterior domain with cracks and singularities at the edges,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 340310, 18 pages, 2012.