Hölder regularity of the solution to the complex Monge-Ampère equation with L p density

On a smooth domain Ω⊂⊂Cn, we consider the Dirichlet problem for the complex Monge-Ampère equation ((ddcu)n=fdV,u|bΩ≡ϕ). We state the Hölder regularity of the solution u when the boundary value ϕ is Hölder continuous and the density f is only Lp, p>1. Note that in former literature (Guedj-Kolodzie...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2016-08, Vol.55 (4), p.1-8
Main Authors: Baracco, Luca, Tran, Vu Khanh, Pinton, Stefano, Zampieri, Giuseppe
Format: Article
Language:English
Subjects:
Density
Dirichlet problem
Monge-Ampere equation
Regularity
Online Access:Get full text
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Summary:On a smooth domain Ω⊂⊂Cn, we consider the Dirichlet problem for the complex Monge-Ampère equation ((ddcu)n=fdV,u|bΩ≡ϕ). We state the Hölder regularity of the solution u when the boundary value ϕ is Hölder continuous and the density f is only Lp, p>1. Note that in former literature (Guedj-Kolodziej-Zeriahi) the weakness of the assumption f∈Lp was balanced by taking ϕ∈C1,1 (in addition to assuming Ω strongly pseudoconvex).
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-016-1008-5