Nonlinear oblique boundary value problems for hessian equations in two dimensions

 Access to full text

 Full (PDF)

1. [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. Zbl0598.35047MR739925
2. [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. Zbl0654.35031MR806416
3. [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. Zbl0347.35019MR437805
4. [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. Zbl0778.35037MR1136351
5. [5] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, Second edition, 1983. Zbl0562.35001MR737190
6. [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. Zbl0522.35028MR718679
7. [7] G.M. Lieberman, Two-dimensional nonlinear boundary value problems for elliptic equations, Trans. Amer. Math. Soc., Vol. 300, 1987, pp. 287-295. Zbl0627.35038MR871676
8. [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. Zbl0619.35047MR833695
9. [9] P.L. Lions, Sur les équations de Monge-Ampère I, Manuscripta Math., Vol. 41, 1983, pp. 1-44. Zbl0509.35036MR689131
10. [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. Zbl0604.35027MR840340
11. [11] A.V. Pogorelov, Monge-Ampère equations of elliptic type, Groningen, Noordhoff, 1964. Zbl0133.04902MR180763
12. [12] A.V. Pogorelov, The Minkowski multidimensional problem, J. Wiley, New York, 1978. Zbl0387.53023
13. [13] N.S. Trudinger, On degenerate fully nonlinear elliptic equations in balls, Bull. Aust. Math. Soc., Vol. 35, 1987, pp. 299-307. Zbl0611.35028MR878440
14. [14] N.S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rat. Mech. Anal., Vol. 111, 1990, pp. 153-179. Zbl0721.35018MR1057653
15. [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. Zbl0524.35047MR729009
16. [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. Zbl0649.35038MR924435
17. [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. Zbl0724.35028MR1089043

1. Ph. Delanoë, Erratum to : “Classical solvability in dimension two of the second boundary value problem associated with the Monge–Ampère operator”