Inventiones mathematicae

, Volume 61, Issue 1, pp 67–79

Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations

  • Neil S. Trudinger


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  1. 1.
    Aleksandrov, A.D.: Majorization of solutions of second-order linear equations, Vestnik Leningrad. Univ.21, 5–25 (1966) English translation in Amer. Math. Soc. Transl. (2)68, 120–143 (1968)Google Scholar
  2. 2.
    Bakel'man, I.Ya.: Theory of quasilinear elliptic equations. Siberian Math. J.2, 179–186 (1961)MATHMathSciNetGoogle Scholar
  3. 3.
    Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer Verlag 1977MATHGoogle Scholar
  4. 4.
    Krylov, N.V., Safonov, M.V.: An estimate of the probability that a diffusion process hits a set of positive measure. Dokl. Akad. Nauk SSSR245, 253–255. English translation in Soviet Math. Dokl.20, 253–255 (1979)MathSciNetGoogle Scholar
  5. 5.
    Krylov, N.V., Safonov, M.V.: Certain properties of solutions of parabolic equations with measurable coefficients. Izvestia Akad. Nauk SSSR40, 161–175 (1980)MathSciNetGoogle Scholar
  6. 6.
    Ladyzhenskaya, O.A., Ural'tseva, N.N.: Linear and quasilinear elliptic equations. Moscow: Izdat. Nauka 1964. English translation: New York: Academic Press 1968MATHGoogle Scholar
  7. 7.
    Pucci, C.: Limitazione per soluzioni di equazioni ellitiche. Ann. Mat. Pura Appl.74, 15–30 (1966)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Serrin, J.: Local behavior of solutions of quasilinear elliptic equations. Acta Math.111, 247–302 (1964)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Serrin, J.: Gradient estimates for solutions of nonlinear elliptic and parabolic equations. In: Contributions to nonlinear functional analysis. pp 565–604, New York: Academic PressGoogle Scholar
  10. 10.
    Trudinger, N.S.: On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math.20, 721–747 (1967)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Neil S. Trudinger
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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