scholarly journals Hölder continuous solutions to the complex Monge–Ampère equations in non-smooth pseudoconvex domains

2017 ◽  
Vol 8 (3) ◽  
pp. 465-484 ◽  
Author(s):  
Nguyen Xuan Hong ◽  
Tran Van Thuy
Keyword(s):  
Pseudoconvex Domains ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Monge Ampere

Existence and Hölder continuity to solutions of the complex Monge–Ampère-type equations with measures vanishing on pluripolar subsets

2021 ◽  
Author(s):  
Le Mau Hai ◽  
Vu Van Quan
Keyword(s):  
Pseudoconvex Domain ◽  
Hölder Continuity ◽  
Type Equation ◽  
Holder Continuity ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Strictly Pseudoconvex Domain ◽  
Monge Ampere

In this paper, we establish existence of Hölder continuous solutions to the complex Monge–Ampère-type equation with measures vanishing on pluripolar subsets of a bounded strictly pseudoconvex domain [Formula: see text] in [Formula: see text].

scholarly journals Hölder continuous solutions to Monge–Ampère equations

2014 ◽  
Vol 16 (4) ◽  
pp. 619-647 ◽  
Author(s):  
Jean-Pierre Demailly ◽  
Sławomir Dinew ◽  
Vincent Guedj ◽  
Pham Hoang Hiep ◽  
Sławomir Kołodziej ◽  
...  
Keyword(s):  
Continuous Solutions ◽  
Hölder Continuous ◽  
Monge Ampere

scholarly journals Hölder continuous solutions to Monge-Ampère equations

2008 ◽  
Vol 40 (6) ◽  
pp. 1070-1080 ◽  
Author(s):  
V. Guedj ◽  
S. Kolodziej ◽  
A. Zeriahi
Keyword(s):  
Continuous Solutions ◽  
Hölder Continuous ◽  
Monge Ampere

scholarly journals Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen
Keyword(s):  
Hermitian Manifold ◽  
General Measure ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hermitian Manifolds ◽  
Right Hand ◽  
The Right ◽  
Monge Ampere ◽  
Compact Hermitian Manifold

AbstractWe prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.

scholarly journals Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds

2018 ◽  
Vol 68 (7) ◽  
pp. 2951-2964 ◽  
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen
Keyword(s):  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hermitian Manifolds ◽  
Monge Ampere

scholarly journals Continuous solutions to two iterative functional equations

2021 ◽  
Author(s):  
Karol Baron
Keyword(s):  
Probability Measure ◽  
Functional Equations ◽  
Continuous Functions ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hölder Continuous Functions

AbstractBased on iteration of random-valued functions we study the problem of solvability in the class of continuous and Hölder continuous functions $$\varphi $$ φ of the equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ \varphi (x)=F(x)+\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ), \end{aligned}$$ φ ( x ) = F ( x ) - ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , φ ( x ) = F ( x ) + ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , where P is a probability measure on a $$\sigma $$ σ -algebra of subsets of $$\Omega $$ Ω .

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