77
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

The Dirichlet problem for an elliptic singular equation

ORCID Icon
Pages 1210-1218 | Received 29 Dec 2018, Accepted 18 Feb 2019, Published online: 23 May 2019

References

  • Weinstein A. Discontinuous integrals and generalized theory of potential. Trans Am Math Soc. 1948;63(2):342–354. doi: 10.1090/S0002-9947-1948-0025023-X
  • Weinstein A. Generalized axially symmetric potential theory. Bull Am. 1953;59:20–38. doi: 10.1090/S0002-9904-1953-09651-3
  • Kipriyanov IA. Singular elliptic boundary problems. Moscow: Nauka; 1997. (In Russian).
  • Kapilevich MB. On the theory of degenerate elliptic differential equations of Bessels class. Dokl Akad Nauk SSSR. 1959;125(4):719–22. (In Russian).
  • Kapilevich MB. On an equation of mixed elliptic-hyperbolic type. Mat Sb. 1952;30(72):11–38. (In Russian).
  • Katrakhov VV, Sitnik SM. The transmutation method and boundary-value problems for singular elliptic equations. Contemp Math Fund Directions. 2018;4(2):211–426. (In Russian).
  • Katrakhov VV, Sitnik SM. Composition method for constructing B-elliptic, B-hyperbolic, and B-parabolic transformation operators. Russ Acad Sci, Dokl Math. 1995;50(1):70–77.
  • Fitouhi A, Jebabli I, Shishkina EL, et al. Applications of integral transforms composition method to wave-type singular differential equations and index shift transmutations. Electron J Differ Equ. 2018;130:1–27.
  • Levitan BM. Expansion in Fourier series and integrals with bessel functions. Uspekhi Mat Nauk. 1951;6(42):102–143. (In Russian).
  • Watson GN. A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press; 1922.
  • Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series, Vol. 2, Special Functions. Gordon and Breach Sci Publ, New York; 1990.
  • Morawetz CM. Mixed equations and transonic flow. J Hyper Diff Eqs. 2004;1:1–26. doi: 10.1142/S0219891604000081
  • Otway T. The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type2043. Berlin, Heidelberg: Springer-Verlag; 2012Series: Lecture notes in mathematics
  • Hristov T, Nikolov A, Popivanov N, et al. Generalized solutions of Protter problem for (3+1)-D Keldysh type equations. AIP Conference Proceedings. 2016;1789, 040007:1–14. (2016).
  • Berezin FA, Faddeev LD. A Remark on Schrödinger's equation with a singular potential. Dokl Akad Nauk Ser Fiz. 1961;137:1011–1014.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.