Ukrainian Mathematical Journal

, Volume 59, Issue 7, pp 955–975 | Cite as

On one boundary-value problem for a strongly degenerate second-order elliptic equation in an angular domain

  • B. V. Bazalii
  • S. P. Degtyarev


We prove the existence and uniqueness of a classical solution of a singular elliptic boundary-value problem in an angular domain. We construct the corresponding Green function and obtain coercive estimates for the solution in the weighted Hölder classes.


Bessel Function Green Function Elliptic Equation Homogeneous Problem Asymptotic Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. A. Kondrat’ev, “Boundary-value problems for elliptic equations in domains with conic or angular points,” Tr. Mosk. Mat. Obshch., 16, 209–292 (1967).zbMATHGoogle Scholar
  2. 2.
    S. Z. Levendorskii and B. G. Paneyakh, “Degenerate elliptic equations and boundary-value problems,” in: VINITI Series in Contemporary Problems of Mathematics (Fundamental Trends) [in Russian], Vol. 63, VINITI, Moscow (1990), pp. 131–200.Google Scholar
  3. 3.
    M. I. Matiichuk, Parabolic and Elliptic Boundary-Value Problems with Singularities [in Ukrainian], Prut, Chernivtsi (2003).Google Scholar
  4. 4.
    P. Grisvard, Elliptic Problem in Nonsmooth Domain, Pitman, London (1985).Google Scholar
  5. 5.
    V. Maz’ya, S. Nazarov, and B. Plamenevskij, Asymptotic Theory of Elliptic Boundary-Value Problems in Singular Perturbed Domains, Birkhäuser, Basel (2000).Google Scholar
  6. 6.
    C. Goalaouic and N. Shimakura, “Regularite Hölderienne de certains problemes aux limites ellipticues degeneres,” Ann. Scuola Norm. Super. Pisa. IV, 10, No. 1 79–108 (1983).Google Scholar
  7. 7.
    D. Gubelidze, “On a generalized solution of the second-order degenerate elliptic equation in an angular domain,” Proc. A. Razmadze Math. Inst., 133, 37–61 (2003).zbMATHMathSciNetGoogle Scholar
  8. 8.
    B. V. Bazalii and N. V. Krasnoshchek, “Regularity of a solution of a multidimensional problem with free boundary for the equation of porous medium,” Mat. Tr., 5, No. 2, 38–91 (2002).MathSciNetGoogle Scholar
  9. 9.
    I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
  10. 10.
    M. V. Fedoryuk, Saddle-Point Method [in Russian], Nauka, Moscow (1977).zbMATHGoogle Scholar
  11. 11.
    O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).Google Scholar
  12. 12.
    B. V. Bazalii and N. V. Krasnoshchek, “Regularity of a solution of a problem with free boundary for the equation υt = (υm)xx,” Alg. Analiz, 12, Issue 2, 1–21 (2000).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • B. V. Bazalii
    • 1
  • S. P. Degtyarev
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian Academy of SciencesDonetsk

Personalised recommendations