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Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations. (English) Zbl 0453.35028


MSC:

35J60 Nonlinear elliptic equations
35B45 A priori estimates in context of PDEs
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References:

[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)
[2] Bakel’man, I.Ya.: Theory of quasilinear elliptic equations. Siberian Math. J.2, 179–186 (1961)
[3] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer Verlag 1977 · Zbl 0361.35003
[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) · Zbl 0459.60067
[5] Krylov, N.V., Safonov, M.V.: Certain properties of solutions of parabolic equations with measurable coefficients. Izvestia Akad. Nauk SSSR40, 161–175 (1980)
[6] Ladyzhenskaya, O.A., Ural’tseva, N.N.: Linear and quasilinear elliptic equations. Moscow: Izdat. Nauka 1964. English translation: New York: Academic Press 1968
[7] Pucci, C.: Limitazione per soluzioni di equazioni ellitiche. Ann. Mat. Pura Appl.74, 15–30 (1966) · Zbl 0144.35801
[8] Serrin, J.: Local behavior of solutions of quasilinear elliptic equations. Acta Math.111, 247–302 (1964) · Zbl 0128.09101
[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 Press
[10] Trudinger, N.S.: On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math.20, 721–747 (1967) · Zbl 0153.42703
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