On the solution of the monge-ampere equation ZxxZyy-Z2xy = f(x,y) with quadratic right side

Please use this identifier to cite or link to this item: http://hdl.handle.net/11452/24534

Title:	On the solution of the monge-ampere equation ZxxZyy-Z2xy = f(x,y) with quadratic right side
Authors:	Aminov, Yu A. Bayram, Bengü Kılıç Öztürk, Günay Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı. 0000-0001-5861-0184 0000-0002-1440-7050 Arslan, Kadri Bulca, Betül Murathan, Cengizhan ABH-3658-2020 AAG-7693-2021 AAG-8775-2021 6603079141 35226209600 6506718146
Keywords:	Mathematics Physics Monge-Ampere equation Polynomial Convex surface
Issue Date:	2011
Publisher:	B Verkin Inst Low Temperature Physics & Engineering Nas Ukra
Citation:	Aminov, Y. vd. (2011). "On the solution of the monge-ampere equation ZxxZyy-Z2xy = f(x,y) with quadratic right side". Journal of Mathematical Physics, Analysis, Geometry, 7(3), 203-211.
Abstract:	For the Monge-Ampere equation Z(xx)Z(yy) - Z(xy)(2) = b(20)(x2)+b(11).xy+b(02y)(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 4b(20)b(02) - b(11)(2) > 0, then the solution also does not exist. If 4b(20)b(02) - b(11)(2) = 0, then we have solutions.
URI:	http://hdl.handle.net/11452/24534
ISSN:	1812-9471 1817-5805
Appears in Collections:	Scopus Web of Science

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