Levi-equation in higher dimensions

Zbginiew Slodkowski; Giuseppe Tomassini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 4, page 277-279
  • ISSN: 1120-6330

Abstract

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We announce some results concerning the Dirichlet problem for the Levi-equation in C n . We consider for the sake of simplicity the case n = 3 .

How to cite

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Slodkowski, Zbginiew, and Tomassini, Giuseppe. "Levi-equation in higher dimensions." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.4 (1991): 277-279. <http://eudml.org/doc/244335>.

@article{Slodkowski1991,
abstract = {We announce some results concerning the Dirichlet problem for the Levi-equation in \( \mathbb\{C\}^\{n\} \). We consider for the sake of simplicity the case \( n = 3 \).},
author = {Slodkowski, Zbginiew, Tomassini, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Levi form; Monge-Ampère equation; Dirichlet problem},
language = {eng},
month = {12},
number = {4},
pages = {277-279},
publisher = {Accademia Nazionale dei Lincei},
title = {Levi-equation in higher dimensions},
url = {http://eudml.org/doc/244335},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Slodkowski, Zbginiew
AU - Tomassini, Giuseppe
TI - Levi-equation in higher dimensions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/12//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 4
SP - 277
EP - 279
AB - We announce some results concerning the Dirichlet problem for the Levi-equation in \( \mathbb{C}^{n} \). We consider for the sake of simplicity the case \( n = 3 \).
LA - eng
KW - Levi form; Monge-Ampère equation; Dirichlet problem
UR - http://eudml.org/doc/244335
ER -

References

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  1. BEDFORD, E. - GAVEAU, B., Envelopes of holomorphy of certain 2-spheres in C 2 . Amer. J. Math., 105, 1983, 975-1009. Zbl0535.32008MR708370DOI10.2307/2374301
  2. BEDFORD, E. - KLINGENBERG, W., On the envelope of holomorphy of a 2-sphere in C 2 . To appear. Zbl0736.32009MR1094437DOI10.2307/2939272
  3. GAVEAU, B., Méthodes de contrôle optimal en analyse complexe. I. Résolution d'équations de Monge-Ampère. J. Funct. Anal., 25, 1977, 391-411. Zbl0356.35071MR457783
  4. GILBARG, D. - TRUDINGER, N. S., Elliptic partial differential equations of second order. Grundlehren Math. Wiss., 224, Springer, 1983. Zbl0562.35001MR737190
  5. LUPACCIOLU, G., A Theorem on holomorphic extension of CR-functions. Pacific J. Math., vol. 124, n. 1, 1986, 177-191. Zbl0597.32014MR850675
  6. SLODKOWSKI, Z., Local maximum property and q-plurisubharmonic functions in uniform algebras. J. Math. Anal. Appl., 115, 1986, 105-130. Zbl0646.46047MR835588DOI10.1016/0022-247X(86)90027-2
  7. SLODKOWSKI, Z. - TOMASSINI, G., Weak solutions for the Levi-equation and envelope of holomorphy. J. Funct. Anal., to appear. Zbl0744.35015MR1136942DOI10.1016/0022-1236(91)90164-Z
  8. TOMASSINI, G., Geometric properties of solutions of the Levi equation. Ann Mat. Pura Appl., (IV), vol. 152, 1988, 331-344. Zbl0681.35017MR980986DOI10.1007/BF01766155

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