On the Solution of the Monge-Ampere Equation ZxxZyy - Zxy 2= f ( x , y ) with Quadratic Right Side

Yu. Aminov; K. Arslan; B. Bulca; C. Murathan; B. (Kilic?) Bayram; G. ?ztürk

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On the Solution of the Monge-Ampere Equation Z_xxZ_yy - Z_xy ²= f ( x , y ) with Quadratic Right Side

机译：关于Monge-Ampere方程Z _{xx Z _{yy -Z _{xy ^{2 = f（x， y），二次方为右侧}}}}

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For the Monge-Ampere equation Z_xxZ_yy - Z ²_xy = b ₂₀ x ²+ b ₁₁ xy + b ₀₂ y ²+ b ₀₀ 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 4 b ₂₀ b ₀₂ - b ²₁₁ > 0, then the solution also does not exist. If 4 b ₂₀ b ₀₂ - b ²₁₁ = 0, then we have solutions.

机译：对于Monge-Ampere方程Z _{xx Z _{yy -Z ^{2 _{xy = b _{20 x ^{2 + b _{11 xy + b _{02 y ^{2 + b _{00 我们考虑在多项式类中存在解Z（x，y）的问题，使得Z = Z（x，y）是凸曲面的图。如果Z是奇数次多项式，则解不存在。如果Z是4级多项式且4 b _{20 b _{02 -b ^{2 _{11 20 b _{02 -b ^{2 _{11 = 0，那么我们有解决方案。}}}}}}}}}}}}}}}}}

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《Journal of Mathematical Physics, Analysis, Geometry》 |2011年第3期|共9页
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Yu. Aminov; K. Arslan; B. Bulca; C. Murathan; B. (Kilic?) Bayram; G. ?ztürk;
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On the Solution of the Monge-Ampere Equation ZxxZyy - Zxy 2= f ( x , y ) with Quadratic Right Side

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On the Solution of the Monge-Ampere Equation Z_xxZ_yy - Z_xy ²= f ( x , y ) with Quadratic Right Side