On the Solution of the Monge-Ampere Equation Z(xx)Z(yy)-Z(xy)(2)=f(x, y) with Quadratic Right Side


Aminov Y., Arslan K., Bayram B. (. , Bulca B., Murathan C., Ozturk 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
  • Keywords: Monge-Ampere equation, polynomial, convex surface
  • Bursa Uludag University Affiliated: Yes

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.