@article{AIHPC_1986__3_3_209_0, author = {Urbas, John I. E.}, title = {The generalized Dirichlet problem for equations of Monge-Amp\`ere type}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {3}, year = {1986}, pages = {209-228}, mrnumber = {847307}, zbl = {0602.35038}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1986__3_3_209_0} }
Urbas, John I. E. The generalized Dirichlet problem for equations of Monge-Ampère type. Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) pp. 209-228. http://gdmltest.u-ga.fr/item/AIHPC_1986__3_3_209_0/
[1] Die innere Geometrie der konvexen Flächen, Akademie-Verlag, Berlin, 1955. | MR 71041 | Zbl 0065.15102
,[2] Dirichlet's problem for the equation Det ∥zij∥ = φ(z1, ..., zn, z, x1, ..., xn), Vestnik Leningrad Univ., t. 13, 1958, p. 5-24, (Russian). | Zbl 0114.30202
,[3] Generalized solutions of the Monge-Ampère equations, Dokl. Akad. Nauk SSSR, t. 114, 1957, p. 1143-1145, (Russian). | MR 95481 | Zbl 0114.29602
,[4] Theory of quasilinear elliptic equations, Sibirsk. Mat. Ž., t. 2, 1961, p. 179-186, (Russian). | MR 126604 | Zbl 0100.30503
,[5] The Dirichlet problem for the elliptic n-dimensional Monge-Ampère equations and related problems in the theory of quasilinear equations, Proceedings of Seminar on Monge-Ampère Equations and Related Topics, (Firenze 1980), Instituto Nazionale di Alta Matematica, Roma, 1982, p. 1-78. | Zbl 0524.53039
,[6] Theorie der konvexen Körper, Springer, Berlin, 1934. | JFM 60.0673.01 | MR 344997 | Zbl 0008.07708
, ,[7] Convex surfaces, Interscience, New York, 1958. | MR 105155 | Zbl 0196.55101
,[8] The Dirichlet problem for nonlinear second order elliptic equations, I. Monge-Ampère equation, Comm. Pure Appl. Math., t. 37, 1984, p. 369-402. | MR 739925 | Zbl 0598.35047
, , ,[9] On the regularity of the Monge-Ampère equation det (∂2u/∂xi∂xj) = F(x, u), Comm. Pure Appl. Math., t. 30, 1977, p. 41-68. | MR 437805 | Zbl 0347.35019
, ,[10] Classical solutions of fully nonlinear, convex, second order elliptic equations, Comm. Pure Appl. Math., t. 35, 1982, p. 333-363. | MR 649348 | Zbl 0469.35022
,[11] On the Dirichlet problem for surfaces of prescribed mean curvature, Manuscripta Math., t. 12, 1974, p. 73-86. | MR 336532 | Zbl 0276.35038
,[12] Elliptic partial differential equations of second order, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, Second Edition, 1983. | MR 737190 | Zbl 0562.35001
, ,[13] Classical solvability of the Dirichlet problem for the Monge-Ampère equation, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), t. 131, 1983, p. 72-79. | MR 718679 | Zbl 0522.35028
,[14] Boundedly inhomogeneous elliptic and parabolic equations in a domain, Izv. Akad. Nauk SSSR, t. 47, 1983, p. 75-108, (Russian). | MR 688919 | Zbl 0578.35024
,[15] Sur les équations de Monge-Ampère I, Manuscripta Math., t. 41, 1983, p. 1-44. | MR 689131 | Zbl 0509.35036
,[16] Sur les équations de Monge-Ampère II, Arch. Rational Mech. Anal. (to appear). | MR 786541 | Zbl 0579.35027
,[17] Monge-Ampère equations of elliptic type, Noordhoff, Gröningen, 1964. | MR 180763 | Zbl 0133.04902
,[18] On the regularity of generalized solutions of the equation det (∂2u/∂xi∂xj) = φ(x1, ..., xn) > 0, Dokl. Akad. Nauk SSSR, t. 200, 1971, p. 543-547, (Russian). English translation in Soviet Math. Dokl., t. 12, 1971, p. 1436- 1440. | MR 293227 | Zbl 0246.35014
,[19] The Dirichlet problem for the n-dimensional analogue of the Monge-Ampère equation, Dokl. Akad. Nauk SSSR, t. 201, 1971, p. 790-793, (Russian). English translation in Soviet Math. Dokl, t. 12, 1971, p. 1727-1731. | MR 293228 | Zbl 0238.35071
,[20] The Minkowski multidimensional problem, J. Wiley, New York, 1978.
,[21] The Dirichlet problem for the multidimensional Monge-Ampère equation, Rocky Mountain J. Math., t. 7, 1977, p. 345-364. | MR 454331 | Zbl 0367.35025
, ,[22] The regularity of conver regions with a metric that is regular in the Hölmer classes, Sibirsk. Mat. Ž., t. 17, 1976, p.907-915, (Russian). English translation in Siberian Math. J., t. 17, 1976, p. 681-687. | MR 425854 | Zbl 0356.53017
,[23] Über die Differentialgleichung rt - s2 = f und das Weylsche Einbettungsproblem, Math. Z., t. 179, 1982, p. 1-10. | MR 643043 | Zbl 0535.35021
,[24] Fully nonlinear, uniformly elliptic equations under natrual structure conditions, Trans. Amer. Math. Soc., t. 278, 1983, p. 751-770. | MR 701522 | Zbl 0518.35036
,[25] The Dirichlet problem for the equation of prescribed Gauss curvature, Bull. Austral. Math. Soc., t. 28, 1983, p. 217-231. | MR 729009 | Zbl 0524.35047
, ,[26] On second derivative estimates for equations of Monge-Ampère type, Bull. Austral. Math. Soc., t. 30, 1984, p. 321-334. | MR 766792 | Zbl 0557.35054
, ,[27] Elliptic equations of Monge-Ampère type, Thesis, Australian National University, 1984.
,[28] The equation of prescribed Gauss curvature without boundary conditions, J. Differential Geometry, t. 20, 1984, p. 311-327. | MR 788283 | Zbl 0566.53013
,[29] Global Hölder estimates for equation of Monge-Ampère type, (to appear). | MR 918234 | Zbl 0674.35026
,