Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Francesca Da Lio; Annamaria Montanari[1]
- [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 (2006)
- Volume: 23, Issue: 1, page 1-28
- ISSN: 0294-1449
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topDa Lio, Francesca, and Montanari, Annamaria. "Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature." Annales de l'I.H.P. Analyse non linéaire 23.1 (2006): 1-28. <http://eudml.org/doc/78682>.
@article{DaLio2006,
affiliation = {Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna (Italie)},
author = {Da Lio, Francesca, Montanari, Annamaria},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {1},
pages = {1-28},
publisher = {Elsevier},
title = {Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature},
url = {http://eudml.org/doc/78682},
volume = {23},
year = {2006},
}
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
PB - Elsevier
VL - 23
IS - 1
SP - 1
EP - 28
LA - eng
UR - http://eudml.org/doc/78682
ER -
References
top- [1] Bardi M., Capuzzo Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations, Birkhäuser, Boston, 1997. Zbl0890.49011MR1484411
- [2] Barles G., Solutions de viscosite des equations de Hamilton–Jacobi, Collection “Mathematiques et Applications” de la SMAI, vol. 17, Springer-Verlag, 1994. Zbl0819.35002
- [3] Barles G., A weak Bernstein method for fully nonlinear elliptic equations, Differential Integral Equations4 (2) (1991) 241-262. Zbl0733.35014MR1081182
- [4] Barles G., Da Lio F., Remarks on the Dirichlet and state-constraint problems for quasilinear parabolic equations, Adv. Differential Equations8 (2003) 897-922. Zbl1073.35120MR1989355
- [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. Zbl0928.35049MR1702961
- [6] Bedford E., Gaveau B., Hypersurfaces with bounded Levi form, Indiana Univ. J.27 (5) (1978) 867-873. Zbl0365.32011MR499287
- [7] Citti G., Lanconelli E., Montanari A., Smoothness of Lipschitz continuous graphs with non vanishing Levi curvature, Acta Math.188 (2002) 87-128. Zbl1030.35084MR1947459
- [8] Crandall M.G., Lions P.L., Viscosity solutions of Hamilton–Jacobi–Bellman equations, Trans. Amer. Math. Soc.277 (1983) 1-42. Zbl0599.35024MR690039
- [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. Zbl0755.35015MR1118699
- [10] Da Lio F., Strong comparison results for quasilinear equations in annular domains and applications, Comm. Partial Differential Equations27 (1&2) (2002) 283-323. Zbl0994.35014MR1886961
- [11] D'Angelo J.P., Several Complex Variables and the Geometry of Real Hypersurfaces, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1993. Zbl0854.32001
- [12] Debiard A., Gaveau B., Problème de Dirichlet pour l'équation de Lévi, Bull. Sci. Math. (2)102 (4) (1978) 369-386. Zbl0413.35067MR517769
- [13] Gilgarg D., Trudinger N.S., Elliptic partial differential equations of second order, Grundlehrer Math. Wiss., vol. 224, Springer-Verlag, New York, 1977. Zbl0361.35003MR473443
- [14] Hörmander L., An Introduction to Complex Analysis in Several Variables, Von Nostrand, Princeton, NJ, 1966. Zbl0138.06203MR203075
- [15] Ishii H., Perron' s method for Hamilton–Jacobi equations, Duke Math. J.55 (1987) 369-384. Zbl0697.35030MR894587
- [16] Ishii H., Lions P.L., Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations83 (1) (1990) 26-78. Zbl0708.35031MR1031377
- [17] Hörmander L., Notions of Convexity, Progr. Math., vol. 127, Birkhäuser, Boston, 1994. Zbl0835.32001MR1301332
- [18] Krantz S.G., Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, RI, 2001. Zbl1087.32001MR1846625
- [19] Montanari A., Lanconelli E., Pseudoconvex fully nonlinear partial differential operators. Strong comparison theorems, J. Differential Equations202 (2) (2004) 306-331. Zbl1161.35414MR2068443
- [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. Zbl1217.35082MR2051691
- [21] Range R.M., Holomorphic Functions and Integral Representation Formulas in Several Complex Variables, Springer-Verlag, New York, 1986. Zbl0591.32002MR847923
- [22] Slodkowski Z., Tomassini G., Weak solutions for the Levi equation and envelope of holomorphy, J. Funct. Anal.101 (2) (1991) 392-407. Zbl0744.35015MR1136942
- [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. Zbl0802.35050MR1269612
- [24] Trudinger N.S., The Dirichlet Problem for the prescribed curvature equations, Arch. Rational Mech. Anal.111 (2) (1990) 153-179. Zbl0721.35018MR1057653
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