Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Da Lio, Francesca ; Montanari, Annamaria1
1 Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna (Italie)
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 1, pp. 1-28.
DOI : 10.1016/j.anihpc.2004.10.006
Da Lio, Francesca  ; Montanari, Annamaria 1

1 Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna (Italie) 
@article{AIHPC_2006__23_1_1_0,
     author = {Da Lio, Francesca and Montanari, Annamaria},
     title = {Existence and uniqueness of {Lipschitz} continuous graphs with prescribed {Levi} curvature},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1--28},
     publisher = {Elsevier},
     volume = {23},
     number = {1},
     year = {2006},
     doi = {10.1016/j.anihpc.2004.10.006},
     mrnumber = {2194579},
     zbl = {05024488},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.006/}
}
TY  - JOUR
AU  - Da Lio, Francesca
AU  - Montanari, Annamaria
TI  - Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2006
SP  - 1
EP  - 28
VL  - 23
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.006/
DO  - 10.1016/j.anihpc.2004.10.006
LA  - en
ID  - AIHPC_2006__23_1_1_0
ER  - 
%0 Journal Article
%A Da Lio, Francesca
%A Montanari, Annamaria
%T Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
%J Annales de l'I.H.P. Analyse non linéaire
%D 2006
%P 1-28
%V 23
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.006/
%R 10.1016/j.anihpc.2004.10.006
%G en
%F AIHPC_2006__23_1_1_0
Da Lio, Francesca; Montanari, Annamaria. Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 1, pp. 1-28. doi : 10.1016/j.anihpc.2004.10.006. http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.006/

[1] Bardi M., Capuzzo Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston, 1997. | MR | Zbl

[2] Barles G., Solutions de viscosite des equations de Hamilton-Jacobi, Collection “Mathematiques et Applications” de la SMAI, vol. 17, Springer-Verlag, 1994. | Zbl

[3] Barles G., A weak Bernstein method for fully nonlinear elliptic equations, Differential Integral Equations 4 (2) (1991) 241-262. | MR | Zbl

[4] Barles G., Da Lio F., Remarks on the Dirichlet and state-constraint problems for quasilinear parabolic equations, Adv. Differential Equations 8 (2003) 897-922. | MR | Zbl

[5] Barles G., Rouy E., Souganidis P.E., Remarks on the Dirichlet problem for quasilinear elliptic and parabolic equations, in: Mceneaney W.M., Yin G.G., Zhang Q. (Eds.), Stochastic Analysis, Control, Optimization and Applications. A Volume in Honor of W.H. Fleming, Birkhäuser, Boston, 1999, pp. 209-222. | MR | Zbl

[6] Bedford E., Gaveau B., Hypersurfaces with bounded Levi form, Indiana Univ. J. 27 (5) (1978) 867-873. | MR | Zbl

[7] Citti G., Lanconelli E., Montanari A., Smoothness of Lipschitz continuous graphs with non vanishing Levi curvature, Acta Math. 188 (2002) 87-128. | MR | Zbl

[8] Crandall M.G., Lions P.L., Viscosity solutions of Hamilton-Jacobi-Bellman equations, Trans. Amer. Math. Soc. 277 (1983) 1-42. | MR | Zbl

[9] Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Soc. 27 (1992) 1-67. | MR | Zbl

[10] Da Lio F., Strong comparison results for quasilinear equations in annular domains and applications, Comm. Partial Differential Equations 27 (1&2) (2002) 283-323. | MR | Zbl

[11] D'Angelo J.P., Several Complex Variables and the Geometry of Real Hypersurfaces, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1993. | Zbl

[12] Debiard A., Gaveau B., Problème de Dirichlet pour l'équation de Lévi, Bull. Sci. Math. (2) 102 (4) (1978) 369-386. | MR | Zbl

[13] Gilgarg D., Trudinger N.S., Elliptic partial differential equations of second order, Grundlehrer Math. Wiss., vol. 224, Springer-Verlag, New York, 1977. | MR | Zbl

[14] Hörmander L., An Introduction to Complex Analysis in Several Variables, Von Nostrand, Princeton, NJ, 1966. | MR | Zbl

[15] Ishii H., Perron' s method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987) 369-384. | MR | Zbl

[16] Ishii H., Lions P.L., Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1) (1990) 26-78. | MR | Zbl

[17] Hörmander L., Notions of Convexity, Progr. Math., vol. 127, Birkhäuser, Boston, 1994. | MR | Zbl

[18] Krantz S.G., Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, RI, 2001. | MR | Zbl

[19] Montanari A., Lanconelli E., Pseudoconvex fully nonlinear partial differential operators. Strong comparison theorems, J. Differential Equations 202 (2) (2004) 306-331. | MR | Zbl

[20] Montanari A., Lascialfari F., The Levi Monge-Ampère equation: smooth regularity of strictly Levi convex solutions, J. Geom. Anal. 14 (2) (2004) 331-353. | MR | Zbl

[21] Range R.M., Holomorphic Functions and Integral Representation Formulas in Several Complex Variables, Springer-Verlag, New York, 1986. | MR | Zbl

[22] Slodkowski Z., Tomassini G., Weak solutions for the Levi equation and envelope of holomorphy, J. Funct. Anal. 101 (2) (1991) 392-407. | MR | Zbl

[23] Slodkowski Z., Tomassini G., The Levi equation in higher dimensions and relationships to the envelope of holomorphy, Amer. J. Math. 116 (2) (1994) 479-499. | MR | Zbl

[24] Trudinger N.S., The Dirichlet Problem for the prescribed curvature equations, Arch. Rational Mech. Anal. 111 (2) (1990) 153-179. | MR | Zbl

Cité par Sources :