Hölder continuous solutions to Monge-Ampère equations
Vincent Guedj, Slawomir Kolodziej, Ahmed Zeriahi
Abstract
We study the regularity of solutions to complex Monge-Ampère equations (ddc u)n=f dV, on bounded strongly pseudoconvex domains Ω⊂ n. We show, under a mild technical assumption, that the unique solution u to such an equation is Hölder continuous if the boundary values ϕ are Hölder continuous and the density f belongs to Lp(Ω) for some p>1. This improves previous results by Bedford-Taylor and Kolodziej.
Create a lesson
Related papers
Square Functions and the Complete Crouzeix Conjecture in Dimension Three
Per Åhag, Rafał Czyż, Antti Perälä et al.
On the Levi map of nondegenerate CR submanifolds
Florian Bertrand, Francine Meylan
Smale's Mean Value Conjecture and its Dual Conjecture for Complex Polynomials
Aneesh Jatar, Tuen Wai Ng
Transcendental Numerical Dimension and Rational Quotients in Kähler Geometry
Songchen Liu
Compactness and the essential norm on Bergman spaces of the Siegel upper half-space
Peiyao Li, Congwen Liu, Jiajia Si
Existence of a "maximal" domain of meromorphy for an analytic function outside a polar compact set
Aleksandr Komlov