Geodesic
Dirichlet problem for degenerate elliptic complex Monge-Ampère equation
Electronic journal of differential equations, Tome 2004 (2004)
We consider the Dirichlet problem

$ \det \big({\frac{\partial^2u}{\partial z_i\partial \overline{z_j}}} \big)=g(z,u)\quad\hbox{in }\Omega\,, \quad u\big|_{ \partial \Omega }=\varphi\,, $

where $\Omega$ is a bounded open set of $\mathbb{C}^{n}$ with regular boundary, $g$ and $\varphi$ are sufficiently smooth functions, and $g$ is non-negative. We prove that, under additional hypotheses on $g$ and $\varphi$, if $|\det \varphi _{i\overline{j}}-g|_{C^{s_{\ast}}}$ is sufficiently small the problem has a plurisubharmonic solution.
Classification : 35J70, 32W20, 32W05
Keywords: degenerate elliptic, omplex Monge-Ampère, plurisubharmonic function 
@article{EJDE_2004__2004__a82,
     author = {Kallel-Jallouli,  Saoussen},
     title = {Dirichlet problem for degenerate elliptic complex {Monge-Amp\`ere} equation},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1217.35088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a82/}
}
TY  - JOUR
AU  - Kallel-Jallouli,  Saoussen
TI  - Dirichlet problem for degenerate elliptic complex Monge-Ampère equation
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a82/
LA  - en
ID  - EJDE_2004__2004__a82
ER  - 
%0 Journal Article
%A Kallel-Jallouli,  Saoussen
%T Dirichlet problem for degenerate elliptic complex Monge-Ampère equation
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a82/
%G en
%F EJDE_2004__2004__a82
Kallel-Jallouli,  Saoussen. Dirichlet problem for degenerate elliptic complex Monge-Ampère equation. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a82/