On the smoothness of viscosity solutions of the prescribed Levi-curvature equation

Giovanna Citti; Ermanno Lanconelli; Annamaria Montanari

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1999)

  • Volume: 10, Issue: 2, page 61-68
  • ISSN: 1120-6330

Abstract

top
In this paper a -regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the -solvability of the Dirichlet problem related to the same equation is showed.

How to cite

top

Citti, Giovanna, Lanconelli, Ermanno, and Montanari, Annamaria. "On the smoothness of viscosity solutions of the prescribed Levi-curvature equation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.2 (1999): 61-68. <http://eudml.org/doc/252347>.

@article{Citti1999,
abstract = {In this paper a \( C^\{\infty\} \)-regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the \( C^\{\infty\} \)-solvability of the Dirichlet problem related to the same equation is showed.},
author = {Citti, Giovanna, Lanconelli, Ermanno, Montanari, Annamaria},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Levi equation; Viscosity solutions; Non-linear vector fields; $ C^\{\infty \} $ C ∞ -regularity; Boundary value problem; -solvability; Dirichlet problem},
language = {eng},
month = {6},
number = {2},
pages = {61-68},
publisher = {Accademia Nazionale dei Lincei},
title = {On the smoothness of viscosity solutions of the prescribed Levi-curvature equation},
url = {http://eudml.org/doc/252347},
volume = {10},
year = {1999},
}

TY - JOUR
AU - Citti, Giovanna
AU - Lanconelli, Ermanno
AU - Montanari, Annamaria
TI - On the smoothness of viscosity solutions of the prescribed Levi-curvature equation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/6//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 2
SP - 61
EP - 68
AB - In this paper a \( C^{\infty} \)-regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the \( C^{\infty} \)-solvability of the Dirichlet problem related to the same equation is showed.
LA - eng
KW - Levi equation; Viscosity solutions; Non-linear vector fields; $ C^{\infty } $ C ∞ -regularity; Boundary value problem; -solvability; Dirichlet problem
UR - http://eudml.org/doc/252347
ER -

References

top
  1. Bedford, E. - Gaveau, B., Envelopes of holomorphy of certain 2-spheres in . Am. J. of Math., 105, 1983, 975-1009. Zbl0535.32008MR708370DOI10.2307/2374301
  2. Citti, G., regularity of solutions of the Levi equation. Analyse non Linéaire, Annales de l’I.H.P, 15, 1998, 517-534. Zbl0921.35033MR1632929DOI10.1016/S0294-1449(98)80033-4
  3. Cabré, X. - Caffarelli, L., Fully nonlinear elliptic equations. Amer. Math. Society, Providence1995. Zbl0834.35002MR1351007
  4. Crandall, M. G. - Ishii, H. - Lions, P. L., User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math Soc., (N.S.), 27, 1992, 1-67. Zbl0755.35015MR1118699DOI10.1090/S0273-0979-1992-00266-5
  5. Citti, G. - Montanari, A., Strong solutions for the Levi curvature equation. Advances in Differential Equations, to appear. Zbl1211.35112MR1734545
  6. Citti, G. - Montanari, A., regularity of solutions of an equation of Levi’s type in . Preprint. Zbl1030.35019MR1848050DOI10.1007/s10231-001-8196-z
  7. Folland, G. B. - Stein, E. M., Estimates for the complex and analysis on the Heisenberg group. Comm. Pure Appl. Math., 20, 1974, 429-522. Zbl0293.35012MR367477
  8. Gilgarg, D. - Trudinger, N. S., Elliptic partial differential equations of second order. Springer-Verlag, Berlin-Heidelberg-New York-Tokio1983. Zbl0361.35003MR737190
  9. Range, R. M., Holomorphic functions and integral representations in several complex variables. Springer-Verlag, Berlin-Heidelberg-New York-Tokio1986. Zbl0591.32002MR847923
  10. Slodkowski, Z. - Tomassini, G., Weak solutions for the Levi equation and envelope of holomorphy. J. Funct. Anal, 101, 4, 1991, 392-407. Zbl0744.35015MR1136942DOI10.1016/0022-1236(91)90164-Z

NotesEmbed ?

top

You must be logged in to post comments.