Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 5, p. 443-457
@article{AIHPC_1991__8_5_443_0,
     author = {Delano\"e, Philippe},
     title = {Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Amp\`ere operator},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {8},
     number = {5},
     year = {1991},
     pages = {443-457},
     zbl = {0778.35037},
     mrnumber = {1136351},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1991__8_5_443_0}
}
Delanoë, P. Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator. Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 5, pp. 443-457. http://www.numdam.org/item/AIHPC_1991__8_5_443_0/

[1] A. Agmon, D. Douglis and L. Nirenberg, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions, I. Comm. Pure Appl. Math., Vol. 12, 1959, pp. 623-727; II, Ibid., Vol. 17, 1964, pp. 35- 92. | MR 125307 | Zbl 0093.10401

[2] T. Aubin, Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité, J. Funct. Anal., Vol. 53, 1983, pp. 231-245.

[3] I. Bakel'Man, Generalized Solutions of Monge-Ampère Equations, Dokl. Akad. Nauk. S.S.S.R., Vol. 114:6, 1957, pp. 1143-1145 (in russian). | MR 95481 | Zbl 0114.29602

[4] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet Problem for Nonlinear Second-Order Elliptic Equations I. Monge-Ampère equation, Comm. Pure Appl.Math., Vol. 37, 1984, pp. 369-402. | MR 739925 | Zbl 0598.35047

[5] B. Dacorogna and J. Moser, On a Partial Differential Equation Involving the Jacobian Determinant, Ann. Inst. Henri Poincaré Analyse non linéaire, Vol. 7:1, 1990, pp. 1-26. | Numdam | MR 1046081 | Zbl 0707.35041

[6] P. Delanoë, Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes II, J. Funct. Anal., Vol. 41, 1981, pp. 341-353. | MR 619957 | Zbl 0474.58023

[7] P. Delanoë, Equations de Monge-Ampère en dimension deux, C. R. Acad. Sci. Paris, 294, série I, 1982, pp. 693-696. | MR 666620 | Zbl 0497.35039

[8] P. Delanoë, Plongements radiaux Sn → Rn+1 à courbure de Gauss positive prescrite, Ann. Sci. Ec. Norm. Sup., Vol. 18, 1985, pp. 635-649. | Numdam | MR 839688 | Zbl 0594.53039

[9] P. Delanoë, Remarques sur les variétés localement Hessiennes, Osaka J. Math., Vol. 26, 1989, pp. 65-69. | MR 991282 | Zbl 0754.53021

[10] P. Delanoë, Viscosity Solutions of Eikonal and Lie Equations on Compact Manifolds, Ann. Global Anal. Geom., Vol. 7:2, 1989, pp. 79-83. | MR 1032326 | Zbl 0644.58020

[11] E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differential-gleichungen zweiter Ordnung vom elliptischen Typus, Sitz. Ber. Preuß. Akad. Wissensch. Berlin, Math.-Phys. Kl, Vol. 19, 1927, pp. 147-152. | JFM 53.0454.02

[12] E. Hopf, A Remark on Linear Elliptic Differential Equations of Second Order, Proc. Am. Math. Soc., Vol. 3, 1952, pp. 791-793. | MR 50126 | Zbl 0048.07802

[13] N.M. Ivotchkina, The a priori Estimate ∥u ∥2C(Ω) on Convex Solutions of the Dirichlet problem for the Monge-Ampère Equation, Zapisk. Nautchn. Semin. LOMI, Vol. 96, 1980, pp. 69-79. | Zbl 0472.35040

[14] L.Y. Liao and F. Schulz, Regularity of Solutions of Two-Dimensional Monge-Ampère Equations, Transact. Am. Math. Soc., Vol. 307:1, 1988, pp. 271-277. | MR 936816 | Zbl 0664.35023

[15] G.M. Lieberman and N.S. Trudinger, Nonlinear Oblique Boundary Value Problems for Nonlinear Elliptic Equations, Transact. Am. Math. Soc., 295:2, 1986, pp. 509-546. | MR 833695 | Zbl 0619.35047

[16] P.-L. Lions, N.S. Trudinger and J.I.E. Urbas, The Neumann problem for Equations of Monge-Ampère Type, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 539-563. | MR 840340 | Zbl 0604.35027

[17] L. Nirenberg, On Nonlinear Elliptic Partial Differential Equations and Hölder Continuity, Comm. Pure Appl. Math., Vol. 6, 1953, pp. 103-156. | MR 64986 | Zbl 0050.09801

[18] A.V. Pogorelov, Monge-Ampère Equations of Elliptic Type, Noordhoff Ltd, 1964. | MR 180763 | Zbl 0133.04902

[19] F. Schulz, Boundary Estimates for Solutions of Monge-Ampère Equations in the Plane, Ann. Sc. Norm. Sup. Pisa, Vol. 11:3, 1984, pp. 431-440. | Numdam | MR 785620 | Zbl 0573.35031

[20] K.-S. Tso, Personal Letters from the Chinese University of Hong-Kong sent on July 12, 1988 and on June 7, 1989.

[21] J.I.E. Urbas, The Oblique Derivative Problem for Equations of Monge-Ampère Type in Two Dimensions, Preprint, Courant Institute and CMA at Canberra, 1987. | MR 924435 | Zbl 0649.35038