Skip to main content
SpringerLink
Log in

Harnack's inequality for elliptic equations and the Hölder property of their solutions

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

In the paper one considers second-order elliptic equations with measurable coefficients in nondivergence form. One proves for them Harnack's inequality and one estimates the Hölder exponent of the solutions. One makes no assumption regarding the smallness of the dispersion of the eigenvalues of the matrix of the coefficients of the second-order derivatives.

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. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).

    Google Scholar 

  2. O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Providence (1968).

  3. E. M. Landis, Second Order Equations of Elliptic and Parabolic Type [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  4. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).

    Google Scholar 

  5. L. Nirenberg, “On nonlinear elliptic partial differential equations and Hölder continuity,' Commun. Pure Appl. Math.,6, 103–156 (1953).

    Google Scholar 

  6. H. O. Cordes, “Uber die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen,” Math. Ann.131, 278–312 (1956).

    Google Scholar 

  7. N. V. Krylov and M. V. Safonov, “An estimate of the probability that a diffusion process hits a set of positive measure,” Dokl. Akad. Nauk SSSR,245, No. 1, 18–20 (1979).

    Google Scholar 

  8. A. D. Akeksandrov, “Majorization of solutions of second-order linear equations,” Vestn. Leningr. Univ., Ser. Math. Mekh. Astron., No. 1. 5–25 (1966).

    Google Scholar 

  9. M. de Guzman, Differentiation of Integrals in ℝn, Lecture Notes in Mathematics, No. 481, Springer-Verlag, Berlin (1975).

    Google Scholar 

Download references

Authors
  1. M. V. Safonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 96, pp. 272–287, 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Safonov, M.V. Harnack's inequality for elliptic equations and the Hölder property of their solutions. J Math Sci 21, 851–863 (1983). https://doi.org/10.1007/BF01094448

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01094448

Keywords

Search

Navigation