Boundary regularity for solutions of the equation of prescribed Gauss curvature
Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 5, p. 499-522
@article{AIHPC_1991__8_5_499_0,
     author = {Urbas, John I. E.},
     title = {Boundary regularity for solutions of the equation of prescribed Gauss curvature},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {8},
     number = {5},
     year = {1991},
     pages = {499-522},
     zbl = {0757.35024},
     mrnumber = {1136354},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1991__8_5_499_0}
}
Urbas, J. I. E. Boundary regularity for solutions of the equation of prescribed Gauss curvature. Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 5, pp. 499-522. http://www.numdam.org/item/AIHPC_1991__8_5_499_0/

[1] A.D. Aleksandrov, Die innere Geometrie der konvexen Flächen, Akademie-Verlag, Berlin, 1955. | MR 71041 | Zbl 0065.15102

[2] A.D. Aleksandrov, Dirichlet's Problem for the Equation Det∥zij∥=φ(z1, ... , zn, z, x1,..., xn), Vestnik Leningrad Univ., Vol. 13, 1958, pp. 5-24 (Russian). | Zbl 0114.30202

[3] I.Ya. Bakel'Man, 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, pp. 1-78. | Zbl 0524.53039

[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] S.-Y. Cheng and S.-T. Yau, On the Regularity of the Monge-Ampère Equation det (∂2u/∂xi∂xj)=F(x, u), Comm. Pure Appl. Math., Vol. 30, 1977, pp. 41-68. | MR 437805 | Zbl 0347.35019

[6] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, Second Edition, 1983. | MR 737190 | Zbl 0562.35001

[7] N.M. Ivochkina, An a priori Estimate of ∥u∥C2 (<Ω) for Convex Solutions of the Dirichlet Problem for the Monge-Ampère Equations, Zap. Naucn. Sem. Leningrad, Otdel. Mat. Inst. Steklov (L.O.M.I.), Vol. 96, 1980, pp. 69-79 (Russian). English translation in J. Soviet Math., Vol. 21, 1983, pp. 689-697. | Zbl 0472.35040

[8] N.M. Ivochkina, Classical Solvability of the Dirichlet Problem for the Monge-Ampère Equation, Zap. Naučn. Sem. Leningrad, Otdel. Mat. Inst. Steklov (L.O.M.I.), Vol. 131, 1983, pp. 72-79. | MR 718679 | Zbl 0522.35028

[9] D. Kinderlehrer, L. Nirenberg, Regularity in Free Boundary Problems, Ann. Sc. Norm. Sup. Pisa, Vol. 4, (4), 1977, pp. 373-391. | Numdam | MR 440187 | Zbl 0352.35023

[10] N.V. Krylov, Nonlinear Elliptic and Parabolic Equations of the Second Order, Reidel, Dordrecht, 1987. | Zbl 0619.35004

[11] C.P. Lau and F.H. Lin, The Best Hölder Exponent for Solutions of the Nonparametric Least Area Problem, Indiana Univ. Math. Journal, Vol. 34, 1985, pp. 809-813. | MR 808827 | Zbl 0581.49025

[12] F.H. Lin, Behaviour of Nonparametric Solutions and Free Boundary Regularity, Proceedings of the Centre for Mathematical Analysis, Australian National University, Vol. 12, 1987, pp. 96-116. | MR 924431 | Zbl 0647.35032

[13] F.H. Lin, Boundary Behaviour of Solutions of Area-Type Problems, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 497-502. | Zbl 0649.49020

[14] L. Simon, Boundary Regularity for Solutions of the Nonparametric Least Area Problem, Ann. Math., Vol. 103, 1976, pp. 429-455. | MR 638358 | Zbl 0335.49031

[15] N.S. Trudinger and J.I.E. Urbas, The Dirichlet Problem for the Equation of Prescribed Gauss Curvature, Bull. Austral. Math. Soc., Vol. 28, 1983, pp. 217-231. | MR 729009 | Zbl 0524.35047

[16] J.I.E. Urbas, Elliptic Equations of Monge-Ampère Type, Thesis, Australian National University, 1984.

[17] J.I.E. Urbas, The Equation of Prescribed Gauss Curvature Without Boundary Conditions, J. Differential Geom., Vol. 20, 1984, pp. 311-327. | MR 788283 | Zbl 0566.53013

[18] J.I.E. Urbas, The Generalized Dirichlet Problem for Equations of Monge-Ampère Type, Ann. Inst. Henri-Poincaré - Analyse Non Linéaire, Vol. 3, 1986, pp. 209-228. | Numdam | MR 847307 | Zbl 0602.35038

[19] J.I.E. Urbas, Global Hölder Estimates for Equations of Monge-Ampère Type, Invent. Math., Vol. 91, 1988, pp. 1-29. | MR 918234 | Zbl 0674.35026

[20] J.I.E. Urbas, Regularity of Generalized Solutions of Monge-Ampère Equations, Math. Z., Vol. 197, 1988, pp. 365-393. | MR 926846 | Zbl 0617.35017

J.I.E. Urbas, Regularity of Almost Extremal Solutions of Monge-Ampère Equations, Proceedings of the Royal Society of Edinburgh, Vol. 117 A, 1991, pp. 21-29. | MR 1096216 | Zbl 0735.35036