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

Aminov Y., ARSLAN K., Kiliç Bayram B., BULCA B., MURATHAN C., Öztürk G.

Journal of Mathematical Physics, Analysis, Geometry, vol.7, no.3, pp.203-211, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 3
  • Publication Date: 2011
  • Journal Name: Journal of Mathematical Physics, Analysis, Geometry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.203-211
  • Bursa Uludag University Affiliated: Yes

Abstract

For the Monge-Ampere equation ZxxZyy-Z2xy = b20x2+b11xy + b02y2 + 600 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 - b211 > 0, then the solution also does not exist. If 4b20b02 - b211 = 0, then we have solutions. © Yu. Aminov, K. Arslan, B. (Kiliç) Bayram, B. Bulca, C. Murathan, and G. OÄztuÄrk, 2011.