Nonlinear oblique boundary value problems for hessian equations in two dimensions
Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) no. 5, pp. 507-575.
@article{AIHPC_1995__12_5_507_0,
     author = {Urbas, John},
     title = {Nonlinear oblique boundary value problems for hessian equations in two dimensions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {507--575},
     publisher = {Gauthier-Villars},
     volume = {12},
     number = {5},
     year = {1995},
     mrnumber = {1353259},
     zbl = {0841.35042},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1995__12_5_507_0/}
}
TY  - JOUR
AU  - Urbas, John
TI  - Nonlinear oblique boundary value problems for hessian equations in two dimensions
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1995
SP  - 507
EP  - 575
VL  - 12
IS  - 5
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1995__12_5_507_0/
LA  - en
ID  - AIHPC_1995__12_5_507_0
ER  - 
%0 Journal Article
%A Urbas, John
%T Nonlinear oblique boundary value problems for hessian equations in two dimensions
%J Annales de l'I.H.P. Analyse non linéaire
%D 1995
%P 507-575
%V 12
%N 5
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1995__12_5_507_0/
%G en
%F AIHPC_1995__12_5_507_0
Urbas, John. Nonlinear oblique boundary value problems for hessian equations in two dimensions. Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) no. 5, pp. 507-575. http://archive.numdam.org/item/AIHPC_1995__12_5_507_0/

[1] 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 | Zbl

[2] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations III. Functions of the eigenvalues of the Hessian, Acta Math., Vol. 155, 1985, pp. 261-301. | MR | Zbl

[3] 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 | Zbl

[4] Ph. Delanoë, Classical solvability in dimension two of the second boundary value problem associated with the Monge-Ampère operator, Ann. Inst. Henri Poincarè, Analyse Non Linèaire, Vol. 8, 1991, pp. 443-457. | Numdam | MR | Zbl

[5] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, Second edition, 1983. | MR | Zbl

[6] N.M. Ivochkina, Classical solvability of the Dirichlet problem for the Monge-Ampère equation, Zap. Naučn. Sem. Leningrad Otdel. Mat. Inst. Steklov. (LOMI), Vol. 131, 1983, pp. 72-79. | MR | Zbl

[7] G.M. Lieberman, Two-dimensional nonlinear boundary value problems for elliptic equations, Trans. Amer. Math. Soc., Vol. 300, 1987, pp. 287-295. | MR | Zbl

[8] G.M. Lieberman and N.S. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations, Trans. Amer. Math. Soc., Vol. 295, 1986, pp. 509-546. | MR | Zbl

[9] P.L. Lions, Sur les équations de Monge-Ampère I, Manuscripta Math., Vol. 41, 1983, pp. 1-44. | MR | Zbl

[10] P.L. Lions, N.S. Trudinoer 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 | Zbl

[11] A.V. Pogorelov, Monge-Ampère equations of elliptic type, Groningen, Noordhoff, 1964. | MR | Zbl

[12] A.V. Pogorelov, The Minkowski multidimensional problem, J. Wiley, New York, 1978.

[13] N.S. Trudinger, On degenerate fully nonlinear elliptic equations in balls, Bull. Aust. Math. Soc., Vol. 35, 1987, pp. 299-307. | MR | Zbl

[14] N.S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rat. Mech. Anal., Vol. 111, 1990, pp. 153-179. | MR | Zbl

[15] N.S. Trudinger and J.I.E. Urbas, The Dirichlet problem for the equation of prescribed Gauss curvature, Bull. Aust. Math. Soc., Vol. 28, 1983, pp. 217-231. | MR | Zbl

[16] J.I.E. Urbas, The oblique derivative problem for equations of Monge-Ampère type, Proceedings of the Centre for Mathematical Analysis, Australian National University, Vol. 12, 1987, pp. 171-195. | MR | Zbl

[17] J.I.E. Urbas, On the existence of nonclassical solutions for two classes of fully nonlinear elliptic equations, Indiana Univ. Math. J., Vol. 39, 1990, pp. 355-382. | MR | Zbl