[L'équation de Monge–Ampère complexe sur les domaines faiblement pseudo-convexes]
Nous montrons ici une régularité de Hölder « faible » jusqu'au bord d'une solution du problème de Dirichlet pour l'équation de Monge–Ampère complexe, de donnée dans l'espace , sur un domaine satisfaisant une f-propriété. Cette f-propriété est une condition de théorie du potentiel qui est satisfaite par tous les domaines pseudo-convexes de type fini et de nombreux exemples de type infini.
We show here a “weak” Hölder regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge–Ampère equation with data in the space and Ω satisfying an f-property. The f-property is a potential-theoretical condition that holds for all pseudoconvex domains of finite type and many examples of infinite-type ones.
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@article{CRMATH_2017__355_4_411_0,
author = {Baracco, Luca and Khanh, Tran Vu and Pinton, Stefano},
title = {The complex {Monge{\textendash}Amp\`ere} equation on weakly pseudoconvex domains},
journal = {Comptes Rendus. Math\'ematique},
pages = {411--414},
publisher = {Elsevier},
volume = {355},
number = {4},
year = {2017},
doi = {10.1016/j.crma.2017.02.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.02.004/}
}
TY - JOUR AU - Baracco, Luca AU - Khanh, Tran Vu AU - Pinton, Stefano TI - The complex Monge–Ampère equation on weakly pseudoconvex domains JO - Comptes Rendus. Mathématique PY - 2017 SP - 411 EP - 414 VL - 355 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.02.004/ DO - 10.1016/j.crma.2017.02.004 LA - en ID - CRMATH_2017__355_4_411_0 ER -
%0 Journal Article %A Baracco, Luca %A Khanh, Tran Vu %A Pinton, Stefano %T The complex Monge–Ampère equation on weakly pseudoconvex domains %J Comptes Rendus. Mathématique %D 2017 %P 411-414 %V 355 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.02.004/ %R 10.1016/j.crma.2017.02.004 %G en %F CRMATH_2017__355_4_411_0
Baracco, Luca; Khanh, Tran Vu; Pinton, Stefano. The complex Monge–Ampère equation on weakly pseudoconvex domains. Comptes Rendus. Mathématique, Tome 355 (2017) no. 4, pp. 411-414. doi : 10.1016/j.crma.2017.02.004. http://www.numdam.org/articles/10.1016/j.crma.2017.02.004/
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☆ The research of T.V. Khanh was supported by the Australian Research Council DE160100173.
