Skip to main content
SpringerLink
Log in

Solvability of a Boundary-Value Problem for Degenerate Equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

We consider a boundary-value problem for degenerate equations with discontinuous coefficients and establish the unique strong solvability (almost everywhere) of this problem in the corresponding weighted Sobolev space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Fichera, “On a unified theory of boundary-value problem for elliptic-parabolic equations of second order,” Boundary Problem on Differential Equations, Madison (1960), pp. 97–120.

  2. H. Alt and S. Luchaus, “Quasilinear elliptic-parabolic differential equation,” Math. Z., 183, 311–341 (1983).

    Article  MathSciNet  Google Scholar 

  3. P. Benilan and P. Wilttbold, “On mind and weak solutions of elliptic-parabolic systems,” Adv. Differential Equations, 1, 1053–1073 (1996).

    MathSciNet  Google Scholar 

  4. T. S. Gadjiev and E. R. Gasimova, “On the smoothness of solution of the first boundary-value problem for second-order degenerate elliptic-parabolic equations,” Ukr. Math. Zh., 60, No. 6, 723–736 (2008); English translation: Ukr. Math. J., 60, No. 6, 831–847 (2008).

  5. H. Gajewski and I. V. Skrypnik, “To the uniqueness problem for nonlinear elliptic equations,” Nonlin. Anal., 52, 291–304 (2003).

    Article  MathSciNet  Google Scholar 

  6. H. Gajewski and I. V. Skrypnik, On the Uniqueness of Solution for Nonlinear Parabolic Equations, Preprint, No. 658, WIAS (2003).

  7. S. Chanillo and R. L. Wheeden, “Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal function,” Amer. J. Math., 107, No. 5, 1191–1226 (1985).

    Article  MathSciNet  Google Scholar 

  8. T. S. Gadjiev and M. Kerimova, “Coercive estimate for degenerate elliptic-parabolic equations,” Proc. Inst. Math. Mech. Nat. Acad. Sci. Azerb., 41, No. 1, 123–134 (2015).

    MathSciNet  MATH  Google Scholar 

  9. M. M. Bokalo and G. P. Domanskiy, “The mixed problem for linear elliptic parabolic pseudoparabolic equations,” Mat. Stud., 40, No. 2, 193–197 (2013).

    MathSciNet  Google Scholar 

  10. I. T. Mamedov, “First boundary-value problem for second-order elliptic parabolic equations with discontinuous coefficients,” J. Math. Sci. (N.Y.), 190, No. 1, 104–134 (2013).

    Article  MathSciNet  Google Scholar 

  11. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow (1967).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    T. Gadjiev, M. Kerimova & G. Gasanova

Authors
  1. T. Gadjiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Kerimova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Gasanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Gadjiev.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 4, pp. 435–451, April, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gadjiev, T., Kerimova, M. & Gasanova, G. Solvability of a Boundary-Value Problem for Degenerate Equations. Ukr Math J 72, 495–514 (2020). https://doi.org/10.1007/s11253-020-01797-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-020-01797-8

Search

Navigation