Comptes Rendus
no. 4
Complex analysis/Partial differential equations
The complex Monge–Ampère equation on weakly pseudoconvex domains
[L'équation de Monge–Ampère complexe sur les domaines faiblement pseudo-convexes]

Présenté par : Jean-Pierre Demailly

Luca Baracco1 ; Tran Vu Khanh2 ; Stefano Pinton1
1 Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
2 School of Mathematics and Applied Statistics, University of Wollongong, NSW, 2522, Australia
Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 411-414.

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 Lp, 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 Lp 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.02.004
Luca Baracco 1 ; Tran Vu Khanh 2 ; Stefano Pinton 1

1 Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
2 School of Mathematics and Applied Statistics, University of Wollongong, NSW, 2522, Australia 
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Luca Baracco; Tran Vu Khanh; Stefano Pinton. The complex Monge–Ampère equation on weakly pseudoconvex domains. Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 411-414. doi : 10.1016/j.crma.2017.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/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.

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