Skip to main content
SpringerLink
Log in

Harnack’s Inequality for Harmonic Functions on Stratified Sets

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We prove Harnack’s inequality for nonnegative harmonic functions in the sense of the “soft” Laplacian on a stratified set with flat strata.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4.
Fig. 5.

Similar content being viewed by others

References

  1. Dairbekov N.S., Penkin O.M., and Sarybekova L.O., “An analog of the Sobolev inequality on a stratified set,” St. Petersburg Math. J., vol. 30, no. 5, 869–875 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  2. Dairbekov N.S., Penkin O.M., and Sarybekova L.O., “The Poincaré inequality and \( p \)-connectedness of a stratified set,” Sib. Math. J., vol. 59, no. 6, 1024–1033 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  3. Pham F., Introduction à l’étude topologique des singularités de Landau, Gauthier-Villars Èditeur, Paris (1967) [French].

    MATH  Google Scholar 

  4. Pokornyi Yu.V., Penkin O.M., Pryadiev V.L. et. al, Differential Equations on Geometric Graphs, Fizmatlit, Moscow (2005) [Russian].

    Google Scholar 

  5. Penkin O.M., “About a geometrical approach to multistructures and some qualitative properties of solutions,” in: Partial Differential Equations on Multistructures, Marcel Dekker, New York (2001), 183–191 (Lecture Notes Pure Appl. Math.; vol. 219).

  6. Gilbarg D. and Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer, Berlin, Heidelberg, and New York (2001).

    Book  MATH  Google Scholar 

  7. Oshchepkova S.N. and Penkin O.M., “The mean-value theorem for elliptic operators on stratified sets,” Math. Notes, vol. 81, no. 3, 365-372 (2007).

    MathSciNet  MATH  Google Scholar 

  8. Penkin O.M., Elliptic Equations on Stratified Sets. Doct. (Phys.-Math.) Dissertation, Voronezh University, Voronezh (2003) [Russian].

    MATH  Google Scholar 

  9. Besedina S.V., “The Harnack inequality for an elliptic equation on a stratified set,” Comm. of Voronezh State University Phyz.-Math. Ser., no. 1, 77–81 (2004).

    MATH  Google Scholar 

Download references

Funding

The authors were supported by the Ministry of Science and Education of the Republic of Kazakhstan (Project AP14871251).

Author information

Authors and Affiliations

  1. Suleyman Demirel University, Kaskelen, Kazakhstan

    N S. Dairbekov

  2. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    N S. Dairbekov & O. M. Penkin

  3. Voronezh State University, Voronezh, Russia

    O. M. Penkin & D. V. Savasteev

Authors
  1. N S. Dairbekov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. M. Penkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. V. Savasteev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N S. Dairbekov.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 5, pp. 971–981. https://doi.org/10.33048/smzh.2023.64.506

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dairbekov, N.S., Penkin, O.M. & Savasteev, D.V. Harnack’s Inequality for Harmonic Functions on Stratified Sets. Sib Math J 64, 1137–1144 (2023). https://doi.org/10.1134/S0037446623050063

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446623050063

Keywords

UDC

Search

Navigation