Journal d’Analyse Mathématique

, Volume 4, Issue 1, pp 292–308 | Cite as

On the Harnack inequality for linear elliptic equations

  • James Serrin


Maximum Principle HARNACK Inequality Minorant Region Inhomogeneous Equation Liouville Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Bernstein, Ueber ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus,Math. Zeit., 26 (1927) pp. 551–558.CrossRefzbMATHGoogle Scholar
  2. 2.
    L. Bers and L. Nirenberg, On linear and non-linear elliptic boundary value problems in the plane,Convegno Internazionale sulle Equazioni Derivate Parziali, 1954, pp. 141–167.Google Scholar
  3. 3.
    W. Feller, Ueber die Lösungen der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus.Math. Ann. 102 (1930), pp. 633–649.CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    D. Gilbarg and J. Serrin, On isolated singularities of solutions of second order elliptic differential equations,J. d'Analyse Math. (following in this issue).Google Scholar
  5. 5.
    E. Hopf. Elementare Betrachtungen ueber die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus,Sitzungsberichte Preuss. Akad. Wiss. 19 (1927), pp. 147–152.Google Scholar
  6. 6.
    O. D. Kellogg. Foundations of Potential Theory, Springer, Berlin 1929.Google Scholar
  7. 7.
    L. Lichtenstein, Beitraege zur Theorie der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus. Unendliche Folgen positiver Lösungen,Rend. Circ. Math. Palermo, 33 (1912), pp. 201–211.CrossRefzbMATHGoogle Scholar
  8. 8.
    C. B. Morrey, Second order elliptic systems of differential equations, in Contributions to the theory of partial differential equations,Ann. of Math. Studies No. 33, Princeton, 1954, pp. 101–159.Google Scholar

Copyright information

© Journal d’Analyse Mathématique (B. A. Amirá) 1956

Authors and Affiliations

  • James Serrin
    • 1
  1. 1.University of MinnesotaMinneapolisU.S.A.

Personalised recommendations