Skip to main content
SpringerLink
Log in

Estimate of the Hölder constant for solutions to m-Hessian equations

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

An a priori estimate for the Hölder constant with exponent 0 < α < 1 is obtained for smooth solutions to m-Hessian equations in a closed domain with (m − 1)-convex boundary of class C 2. The Hölder constant depends on the L p-norm, p > [n(n + 1)]/2, of the right-hand side of the equation, and the estimate remains valid for approximate solutions. Bibliography: 4 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.

Similar content being viewed by others

References

  1. N. M. Ivochkina and N. V. Filimonenkova, “Lemma about increase of approximate solutions to the Dirichlet problem for m-Hessian equations” [in Russian], Probl. Mat. Anal. 38, 37–45 (2008); English transl.: J. Math. Sci., New York 156, No. 4, 606–616 (2009).

    Google Scholar 

  2. N. V. Filimonenkova, “Phragmén–Lindelöf type theorem for m-Hessian equations” [in Russian], Probl. Mat. Anal. 39, 147–155 (2009); English transl.: J. Math. Sci., New York 157, No. 6, 948–957 (2009).

    Google Scholar 

  3. L. Caffarelly, L. Nirenberg, and J. Spruck, “The Dirichlet problem for nonlinear second order elliptic equations III. Functions of the eigenvalues of the Hessian,” Acta Math. 155, 261–301 (1985).

    Article  MathSciNet  Google Scholar 

  4. N. S. Trudinger, “Week solutions of Hessian equations,” Commun. Partial Differ. Equ. 22, 1251–1261 (1997).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University of Architecture and Civil Engineering, 2-nd Krasnoarmeiskaia St. 4, St. Petersburg, 190005, Russia

    N. M. Ivochkina & N. V. Filimonenkova

Authors
  1. N. M. Ivochkina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. V. Filimonenkova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. M. Ivochkina.

Additional information

Dedicated to Nina Nikolaevna Uraltseva

Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 69–76.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivochkina, N.M., Filimonenkova, N.V. Estimate of the Hölder constant for solutions to m-Hessian equations. J Math Sci 159, 67–74 (2009). https://doi.org/10.1007/s10958-009-9427-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-009-9427-x

Keywords

Search

Navigation