Skip to main content
SpringerLink
Log in

Convex solutions of certain elliptic equations have constant rank hessians

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

References

  1. Alexandrov, A. D., Majorization of solutions of second order linear equations Vestrik Leningrad Univ., 21 (1966), 5–25. English translation in Am. Math. Soc. Transl. (2) 68 (1968), 120–143.

    Google Scholar 

  2. Caffarelli, L. & A. Friedman, Convexity of solutions of semilinear elliptic equations, Duke Math. J. 52 (1985) 431–456.

    Google Scholar 

  3. Gabriel, R., A result concerning convex level surfaces of 3-dimensional harmonic functions, J. London Math. Soc. 32 (1957), 286–294.

    Google Scholar 

  4. Gilbarg, D. & N. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1977.

  5. Hopf, E., Über der Funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen Zweiter Ordnung, Math. Z. 34 (1932), 194–233.

    Google Scholar 

  6. Kawohl, B. A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem, Lefschetz Center for Dynamical Systems, # 84-6, Brown University, 1984.

  7. Kennington, A. An improved convexity maximum principle and some applications, Ph. D. thesis, University of Adelaide, South Australia, 1984.

    Google Scholar 

  8. Kennington, A. Power concavity and boundary value problems, Indiana Univ. Math. J. 34 (1985) 687–704.

    Google Scholar 

  9. Korevaar, N. Convex solutions to nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 32 (1983), 603–614.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington

    Nicholas J. Korevaar & John L. Lewis

Authors
  1. Nicholas J. Korevaar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John L. Lewis
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. Serrin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korevaar, N.J., Lewis, J.L. Convex solutions of certain elliptic equations have constant rank hessians. Arch. Rational Mech. Anal. 97, 19–32 (1987). https://doi.org/10.1007/BF00279844

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00279844

Keywords

Search

Navigation