Dirichlet problem for degenerate elliptic complex Monge-Ampere equation
We consider the Dirichlet problem $$ det ig({frac{partial^2u}{partial z_ipartial overline{z_j}}} ig)=g(z,u)quadmbox{in }Omega,, quad uig|_{ partial Omega }=varphi,, $$ where $Omega$ is a bounded open set of $mathbb{C}^{n}$ with regular boundary, $g$ and $varphi$ are sufficiently smooth functions, an...
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| Format: | Article |
| Language: | English |
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Texas State University
2004-04-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/48/abstr.html |
| Summary: | We consider the Dirichlet problem $$ det ig({frac{partial^2u}{partial z_ipartial overline{z_j}}} ig)=g(z,u)quadmbox{in }Omega,, quad uig|_{ partial Omega }=varphi,, $$ 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 $|det varphi _{ioverline{j}}-g|_{C^{s_{ast}}}$ is sufficiently small the problem has a plurisubharmonic solution. |
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| ISSN: | 1072-6691 |