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Global regularity of solutions of nonlinear second order elliptic and parabolic differential equations

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References

  1. Evans, L.C.: Classical solutions of fully nonlinear, convex, second order elliptic equations. Comm. Pure Appl. Math.35, 333–363 (1982)

    Google Scholar 

  2. Gilbarg, D., Hörmander, L.: Intermediate Schauder estimates. Arch. Rational Mech. Anal.74, 297–318 (1980)

    Google Scholar 

  3. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, 2nd ed. 1983. Berlin, Heidelberg, New York, Tokyo: Springer 1977

    Google Scholar 

  4. Gruber, M.: Harnack inequalities for solutions of general second order parabolic equations and estimates of their Hölder norms. Math. Z.185, 23–43 (1984)

    Google Scholar 

  5. Krylov, N.V.: Boundedly nonhomogeneous elliptic and parabolic equations. Izv. Akad. Nauk SSSR, Ser. Mat.46, 487–523 (1982) [Russian], English translation in Math. USSR, Izv.20, 459–493 (1983)

    Google Scholar 

  6. Krylov, N.V.: Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Nauk SSSR, Ser. Mat.47, 75–108 (1983) [Russian], English translation in Math. USSR, Izv.21, 67–98 (1984)

    Google Scholar 

  7. Krylov, N.V.: Estimates for derivatives of the solutions of nonlinear parabolic equations. Dokl. Akad. Nauk SSSR274, 23–26 (1984) [Russian], English translation in Sov. Math., Dokl.29, 14–17 (1984)

    Google Scholar 

  8. Ladyzhenskaya, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and quasilinear equations of parabolic type. Izdat. “Nauka” Moscow 1967 [Russian], English Translation: Am. Math. Soc.: Providence, R.I., 1968

    Google Scholar 

  9. Lieberman, G.M.: The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data. Commun. Partial Differ. Equations11, 167–229 (1986)

    Google Scholar 

  10. Lieberman, G.M.: Intermediate Schauder theory for second order parabolic equations, I. Estimates. J. Differ. Equations63, 1–31 (1986)

    Google Scholar 

  11. Lieberman, G.M.: The first-initial-boundary value problem for quasilinear parabolic equations. Ann. Sc. Norm. Super. Pisa, to appear

  12. Lieberman, G.M., Trudinger, N.S.: Nonlinear oblique derivative problems for nonlinear elliptic equations. Trans. Am. Math. Soc.295, 509–546 (1986)

    Google Scholar 

  13. Safonov, M.V.: On the classical solution of Bellman's elliptic equations. Dokl. Akad. Nauk SSSR278, 810–813 (1984) [Russian], English translation in Sov. Math., Dokl.30, 482–485 (1984)

    Google Scholar 

  14. Schulz, F.: Über nichtlineare, konkave elliptische Differentialgleichungen. Math. Z.191, 429–448 (1986)

    Google Scholar 

  15. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton: University Press 1970

    Google Scholar 

  16. Trudinger, N.S.: Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations. Invent. Math.61, 67–79 (1980)

    Google Scholar 

  17. Trudinger, N.S.: Fully nonlinear, uniformly elliptic equations under natural structure conditions. Trans. Am. Math. Soc.278, 751–769 (1983)

    Google Scholar 

  18. Trudinger, N.S.: Regularity of solutions of fully nonlinear elliptic equations. Boll. Unione Mat. Ital., VI. Ser., A3, 421–430 (1984)

    Google Scholar 

  19. Trudinger, N.S.: Regularity of solutions of fully nonlinear elliptic equations. II. Australian National University, Centre for Mathematical Analysis. Research Report R38 (1984)

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Lieberman, G.M. Global regularity of solutions of nonlinear second order elliptic and parabolic differential equations. Math Z 193, 331–346 (1986). https://doi.org/10.1007/BF01229801

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