Skip to main content
SpringerLink
Log in

Analysis of the Existence of Special Solutions to the Capillarity Problem

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

This paper is devoted to the study of the existence of solutions of the capillary equation under the influence of an external potential leading to surface surgery.

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. A. Yu. Borisovich, “The Plateau operator and bifurcations of teo-dimensional minimal surfaces,” in: Global Analysis and Mathematical Physics [in Russian], Voronezh (1987), pp. 142–155.

  2. Dào Trong Thi and A. T. Fomenko, Minimal Surfaces and Plateau’s Problem [in Russian], Nauka, Moscow (1987).

  3. B. M. Darinsky, Yu. I. Sapronov, and S. L. Tsarev, “Bifurcations of extremals of Fredholm functionals,” Sovr. Mat. Fundam. Napr., 12, 3–140 (2004).

    MATH  Google Scholar 

  4. R. Finn, Equilibrium Capillary Surfaces, Springer-Verlag, New York (1986).

    Book  MATH  Google Scholar 

  5. L. Nirenberg, Topics in Nonlinear Functional Analysis, New York Univ., New York (1974).

    MATH  Google Scholar 

  6. L. V. Stenyukhin, “On minimal surfaces with with constraints of inequality type,” Izv. Vyssh. Ucheb. Zaved. Mat., 11, 51–59 (2012).

    MathSciNet  MATH  Google Scholar 

  7. L. V. Stenyukhin, “On specific solutions of the capillarity problem with circular symmetry,” Vestn. Voronezh. State Univ. Ser. Fiz. Mat., 2, 242–245 (2013).

  8. L. V. Stenyukhin, “Bifurcation analysis of the capillarity problem with circular symmetry,” Vestn. Yuzhno-Ural. State Univ. Ser. Mat. Model. Program., 7, No. 2, 77–83 (2014).

    MATH  Google Scholar 

  9. N. N. Uraltseva, “A solution of the capillarity problem,” Vestn. Leningrd. Univ., 19, 54–64 (1973).

    Google Scholar 

  10. H. C. Wente, “The symmetry of sessile and pendent drops,” Pac. J. Math., 88, No. 2, 387–397 (1980).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    L. V. Stenyukhin

Authors
  1. L. V. Stenyukhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. V. Stenyukhin.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stenyukhin, L.V. Analysis of the Existence of Special Solutions to the Capillarity Problem. J Math Sci 267, 781–786 (2022). https://doi.org/10.1007/s10958-022-06169-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-06169-0

Keywords and phrases

AMS Subject Classification

Search

Navigation