On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side
For the Monge{Ampere equation ZxxZyy-Z²xy = b₂₀x²+b₁₁xy+b₀₂y²+b₀₀ we consider the question on the existence of a solution Z(x, y) in the class of polynomials such that Z = Z(x, y) is a graph of a convex surface. If Z is a polynomial of odd degree, then the solution does not exist. If Z is a polynomi...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2011 |
| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106681 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side / Yu. Aminov, K. Arslan, B. Bulca, C. Murathan, B. (Kilic) Bayram, G. Öztürk // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 3. — С. 203-211. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731525716443136 |
|---|---|
| author | Aminov, Yu. Arslan, K. Bulca, B. Murathan, C. Bayram, B. (Kilic) Öztürk, G. |
| author_facet | Aminov, Yu. Arslan, K. Bulca, B. Murathan, C. Bayram, B. (Kilic) Öztürk, G. |
| citation_txt | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side / Yu. Aminov, K. Arslan, B. Bulca, C. Murathan, B. (Kilic) Bayram, G. Öztürk // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 3. — С. 203-211. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | For the Monge{Ampere equation ZxxZyy-Z²xy = b₂₀x²+b₁₁xy+b₀₂y²+b₀₀ we consider the question on the existence of a solution Z(x, y) in the class of polynomials such that Z = Z(x, y) is a graph of a convex surface. If Z is a polynomial of odd degree, then the solution does not exist. If Z is a polynomial of 4-th degree and 4b₂₀b₀₂ - b₁₁² > 0, then the solution also does not exist. If 4b₂₀b₀₂ - b₁₁² = 0, then we have solutions.
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| first_indexed | 2025-12-07T19:27:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106681 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T19:27:12Z |
| publishDate | 2011 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Aminov, Yu. Arslan, K. Bulca, B. Murathan, C. Bayram, B. (Kilic) Öztürk, G. 2016-10-02T19:28:53Z 2016-10-02T19:28:53Z 2011 On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side / Yu. Aminov, K. Arslan, B. Bulca, C. Murathan, B. (Kilic) Bayram, G. Öztürk // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 3. — С. 203-211. — Бібліогр.: 5 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106681 For the Monge{Ampere equation ZxxZyy-Z²xy = b₂₀x²+b₁₁xy+b₀₂y²+b₀₀ we consider the question on the existence of a solution Z(x, y) in the class of polynomials such that Z = Z(x, y) is a graph of a convex surface. If Z is a polynomial of odd degree, then the solution does not exist. If Z is a polynomial of 4-th degree and 4b₂₀b₀₂ - b₁₁² > 0, then the solution also does not exist. If 4b₂₀b₀₂ - b₁₁² = 0, then we have solutions. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side Article published earlier |
| spellingShingle | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side Aminov, Yu. Arslan, K. Bulca, B. Murathan, C. Bayram, B. (Kilic) Öztürk, G. |
| title | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side |
| title_full | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side |
| title_fullStr | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side |
| title_full_unstemmed | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side |
| title_short | On the Solution of the Monge-Ampere Equation ZxxZyy - Z²xy= f (x, y) with Quadratic Right Side |
| title_sort | on the solution of the monge-ampere equation zxxzyy - z²xy= f (x, y) with quadratic right side |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106681 |
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