RIS ID
108445
Abstract
On a smooth domain ⊂⊂ Cn,we consider the Dirichlet problem for the complex Monge-Ampère equation ((ddcu)n = f dV, u|b ≡ φ). We state the Hölder regularity of the solution u when the boundary value φ is Hölder continuous and the density f is only L p, p > 1. Note that in former literature (Guedj-Kolodziej-Zeriahi) the weakness of the assumption f ∈ L p was balanced by taking φ ∈ C1,1 (in addition to assuming strongly pseudoconvex).
Grant Number
ARC/DE160100173
Publication Details
Baracco, L., Khanh, T., Pinton, S. & Zampieri, G. (2016). Hölder regularity of the solution to the complex Monge-Ampère equation with L p density. Calculus of Variations and Partial Differential Equations, 55 (4), 74-1-74-8.