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 |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/48/abstr.html |
| _version_ | 1811245664502284288 |
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| author | Saoussen Kallel-Jallouli |
| author_facet | Saoussen Kallel-Jallouli |
| author_sort | Saoussen Kallel-Jallouli |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T14:42:45Z |
| format | Article |
| id | doaj.art-a6a7882fee8f4569a8d9617429fff141 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T14:42:45Z |
| publishDate | 2004-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-a6a7882fee8f4569a8d9617429fff1412022-12-22T03:28:46ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-04-01200448124Dirichlet problem for degenerate elliptic complex Monge-Ampere equationSaoussen Kallel-JallouliWe 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.http://ejde.math.txstate.edu/Volumes/2004/48/abstr.htmlDegenerate ellipticomplex Monge-AmperePlurisubharmonic function. |
| spellingShingle | Saoussen Kallel-Jallouli Dirichlet problem for degenerate elliptic complex Monge-Ampere equation Electronic Journal of Differential Equations Degenerate elliptic omplex Monge-Ampere Plurisubharmonic function. |
| title | Dirichlet problem for degenerate elliptic complex Monge-Ampere equation |
| title_full | Dirichlet problem for degenerate elliptic complex Monge-Ampere equation |
| title_fullStr | Dirichlet problem for degenerate elliptic complex Monge-Ampere equation |
| title_full_unstemmed | Dirichlet problem for degenerate elliptic complex Monge-Ampere equation |
| title_short | Dirichlet problem for degenerate elliptic complex Monge-Ampere equation |
| title_sort | dirichlet problem for degenerate elliptic complex monge ampere equation |
| topic | Degenerate elliptic omplex Monge-Ampere Plurisubharmonic function. |
| url | http://ejde.math.txstate.edu/Volumes/2004/48/abstr.html |
| work_keys_str_mv | AT saoussenkalleljallouli dirichletproblemfordegenerateellipticcomplexmongeampereequation |