Skip to main content
SpringerLink
Log in

On solvability conditions of the Dirichlet problem form-curvature equations

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

Abstract

This papor contains a refined variant of the Jenkins-Serrin-Trudinger condition related to the Dirichlet problem for curvature equations. The new condition implies the classical solvability of the Gauss curvature equation in the case of positive curvature small enough on the boundary. Bibliography: 8 titles.

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

Literature Cited

  1. L. Caffarelli, L. Nirenberg, and J. Spruck, “Nonlinear second order elliptic equations V. The Dirichet problem for Weingarten hypersurfaces,”Comm. Pure Appl. Math.,41, 47–70 (1988).

    MathSciNet  MATH  Google Scholar 

  2. N. M. Ivochkina, “Solution of the Dirichlet problem form-curvature equation,”Mat. Sb.,180, 867–887 (1989).

    MATH  Google Scholar 

  3. N. M. Ivochkina, “The Dirichlet problem form-curvature equations,”Algebra Analiz,2, 192–217 (1990).

    MATH  MathSciNet  Google Scholar 

  4. N. S. Trudinger, “The Dirichlet problem for the prescribed curvature equations,”Arch. Rat. Mech. Anal.,111, 153–179 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  5. N. M. Ivochkina, “The Dirichlet principle in the theory of the Monge-Ampere equations”Algebra Analiz,4, 131–156 (1992).

    MATH  MathSciNet  Google Scholar 

  6. H. Jenkins and J. Serrin, “The Dirichlet problem for the minimal surface equation in higher dimensions,”J. Reine Angew. Math.,229, 170–187 (1968).

    MathSciNet  MATH  Google Scholar 

  7. J. Serrin, “The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables,”Phil. Trans. Roy. Soc. Lond., Ser A264, 413–496 (1969).

    MATH  MathSciNet  Google Scholar 

  8. N. S. Trudinger and J. Urbas, “On the Dirichlet problem for the prescribed Gauss curvature equations,”Bull. Aus. Math. Soc.,28, 217–231 (1983).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. N. M. Ivochkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to V. A. Solonnikov on his sixtieth anniversary

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 48–65.

Translated by S. A. Titarenko.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivochkina, N.M. On solvability conditions of the Dirichlet problem form-curvature equations. J Math Sci 84, 856–861 (1997). https://doi.org/10.1007/BF02399937

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02399937

Keywords

Search

Navigation