Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 582097, 16 pages
http://dx.doi.org/10.5402/2011/582097
Research Article

On Removable Sets of Solutions of Elliptic Equations

Department of Nonlinear Analyses, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, F. Agaev street, Baku AZ1141, Azerbaijan

Received 8 March 2011; Accepted 20 April 2011

Academic Editors: G. L. Karakostas, G. Mantica, X. B. Pan, and C. Zhu

Copyright © 2011 Tair S. Gadjiev 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. Carleson, Selected Problems on Exceptional Sets, D. Van. Nostrand company, London, UK, 1967.
  2. E. I. Moiseev, “On Neumann problem in piecewise smooth domains,” Differentsial'nye Uravneniya, vol. 7, no. 9, pp. 1655–1656, 1971 (Russian). View at Google Scholar
  3. E. I. Moiseev, “On existence and non-existence boundary sets for the Neumann problem,” Differentsial'nye Uravneniya, vol. 9, no. 5, pp. 901–911, 1973 (Russian). View at Google Scholar
  4. E. M. Landis, “To question on uniqueness of solution of the first boundary value problem for elliptic and parabolic equations of the second order,” Uspekhi Matematicheskikh Nauk, vol. 33, no. 3, p. 151, 1978 (Russian). View at Google Scholar
  5. V. A. Kondratyev and E. M. Landis, “Qualitative theory of linear partial differential equations of second order,” in Modern Problems of Mathematics, Fundamental Directions, Partial Differential Equations, vol. 3 of Itogi nauki i tekhniki, Ser, pp. c99–c212, VINITI, Moscow, Russia, 1988. View at Google Scholar
  6. I. T. Mamedov, “On exceptional sets of solutions of Dirichlet problem for elliptic equations of second order with discontinuous coefficients,” Proceedings of the Institute of Mathematics and Mechanics. Academy of Sciences of Azerbaijan, vol. 8, pp. 137–149, 1998. View at Google Scholar
  7. M. L. Gerver and E. M. Landis, “One generalization of a theorem on wean value for multivariable functions,” Doklady Akademii Nauk SSSR, vol. 146, no. 4, pp. 761–764, 1962 (Russian). View at Google Scholar · View at Zentralblatt MATH
  8. V. Kayzer and B. Muller, “Removable sets for heat conduction,” Vestnik of Moscow University, no. 5, pp. 26–32, 1973 (Russian). View at Google Scholar
  9. V. A. Mamedova, “On removable sets of solutions of boundary value problems for elliptic equations of the second order,” Transactions of National Academy of Sciences of Azerbaijan, vol. 25, no. 1, pp. 101–106, 2005. View at Google Scholar
  10. T. S. Gadjiev and V. A. Mamedova, “On removable sets of solutions of second order elliptic and parabolic equations in nondivergent form,” Ukrainian Mathematical Journal, vol. 61, no. 11, pp. 1485–1496, 2009. View at Google Scholar
  11. T. Kilpeläinen and X. Zhong, “Removable sets for continuous solutions of quasilinear elliptic equations,” Proceedings of the American Mathematical Society, vol. 130, no. 6, pp. 1681–1688, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Diederich, “Removable sets for pointwise solutions of elliptic partial differential equations,” Transactions of the American Mathematical Society, vol. 165, pp. 333–352, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. Harvey and J. Polking, “Removable singularities of solutions of linear partial differential equations,” Acta Mathematica, vol. 125, pp. 39–56, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. B. E. J. Dahlberg, “On exceptional sets at the boundary for subharmonic functions,” Arkiv för Matematik, vol. 15, no. 2, pp. 305–312, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. E. M. Landis, Second Order Equations of Elliptic and Parabolic Types, Nauka, Moscow, Russia, 1971.
  16. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, Germany, 1977.