Literatur
Caffarelli, L., Kohn, J.J., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second order elliptic equations. II. Complex Monge-Ampère, and uniformly elliptic, equations. (Preprint)
Caffarelli, L., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation. Commun. Pure Appl. Math.37, 369–402 (1984)
Calabi, E.: Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens. Mich. Math. J.5, 105–126 (1958)
Evans, L.C.: Classical solutions of fully nonlinear, convex, second-order elliptic equations. Commun. Pure Appl. Math.35, 333–363 (1982)
Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Ann. Math. Stud.105, Princeton, N.J.: Princeton University Press 1983
Giaquinta, M., Hildebrandt, S.: Estimation a priori des solutions faibles de certains systèmes non linéaires elliptiques. Séminaire Goulaouic-Meyer-Schwartz, Exposé no.17, École Polytechnique, Paris 1981
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. 2. Ausgabe, Berlin-Heidelberg-New York-Tokyo: Springer 1983
Grüter, M., Widman, K.-O.: The Green function for uniformly elliptic equations. Manuscr. Math.37, 303–342 (1982)
Hildebrandt, S.: Quasilinear elliptic systems in diagonal form. Vorlesungsreihe no.11, Sonderforschungsbereich 72, Bonn 1982
Krylov, N.V.: Boundedly nonhomogeneous elliptic and parabolic equations. Izv. Akad. Nauk SSSR, Ser. Mat.46, 487–523 (1982) [Russisch]. Engl. Übersetzung in: Math. USSR, Izv.20, 459–492 (1983)
Krylov, N.V.: Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Nauk SSSR, Ser. Mat.47, 75–108 (1983) [Russisch]. Engl. Übersetzung in: Math. USSR, Izv.22, 67–97 (1984)
Krylov, N.V.: On estimates for the derivatives of solutions of nonlinear parabolic equations. Dokl. Akad. Nauk SSSR274, 23–26 (1984), [Russisch]. Engl. Übersetzung in: Soviet Math. Dokl.29, 14–17 (1984)
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, 18–20 (1979) [Russisch]. Engl. Übersetzung in: Soviet Math. Dokl.20, 253–255 (1979)
Krylov, N.V., Safonov, M.V.: A certain property of solutions of parabolic equations with measurable coefficients. Izv. Akad. Nauk SSSR, Ser. Mat.44, 161–175 (1980) [Russisch]. Engl. Übersetzung in: Math. USSR, Izv.16, 151–164 (1981)
Lieberman, G., Trudinger, N.S.: Nonlinear oblique boundary value problems for nonlinear elliptic equations. (Preprint)
Littman, W., Stampacchia, G., Weinberger, H.F.: Regular points for elliptic equations with discontinuous coefficients. Ann. Sc. Norm. Super. Pisa, Cl. Sci., III. Ser.17, 43–77 (1963)
Nirenberg, L.: On nonlinear elliptic partial differential equations and Hölder continuity. Commun. Pure Appl. Math.6, 103–156 (1953)
Pogorelov, A.V.: The Minkowski multidimensional problem. Washington: Winston 1978
Safonov, M.V.: Harnack's inequality for elliptic equations and the Hölder property of their solutions. Zap. Naučhn. Semin. Leningr. Otd. Mat. Inst. Steklova96, 272–287 (1980) [Russisch]. Engl. Übersetzung in: J. Soviet Math.21, 851–863 (1983)
Schulz, F.: Über die Beschränktheit der zweiten Ableitungen der Lösungen nichtlinearer elliptischer Differentialgleichungen. Math. Z.175, 181–188 (1980)
Schulz, F.: A priori estimates for solutions of Monge-Ampère equations. Arch. Rational Mech. Anal.89, 123–133 (1985)
Schulz, F.: A priori estimates and a Liouville theorem for elliptic Monge-Ampère equations. Math. Ann.264, 475–483 (1983)
Schulz, F.: Boundary estimates for solutions of Monge-Ampère equations in the plane. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.11, 431–440 (1984)
Schulz, F.: A remark on fully nonlinear, concave elliptic equations. In: Miniconference on Nonlinear Analysis (Canberra, 5.–7. Juli 1984). Proc. Centre Math. Anal. Australian Nat. Univ.8, pp. 202–207, Canberra 1984
Trudinger, N.S.: Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations. Invent. Math.61, 67–79 (1980)
Trudinger, N.S.: Elliptic equations in non-divergence form. In: Miniconference on Partial Differential Equations (Canberra, 9.–10. Juli 1981). Proc. Centre Math. Anal. Australian Nat. Univ.1, pp. 1–16, Canberra 1982
Trudinger, N.S.: Fully nonlinear, uniformly elliptic equations under natural structure conditions. Trans. Am. Math. Soc.278, 751–769 (1983)
Urbas, J.I.E.: Elliptic equations of Monge-Ampère type. Dissertation, Australian Nat. Univ., Canberra 1984
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Schulz, F. Über nichtlineare, konkave elliptische Differentialgleichungen. Math Z 191, 429–448 (1986). https://doi.org/10.1007/BF01162718
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DOI: https://doi.org/10.1007/BF01162718