On the Solution of the Monge-Ampere Equation Z(xx)Z(yy)-Z(xy)(2)=f(x, y) with Quadratic Right Side
JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, cilt.7, sa.3, ss.203-211, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 7 Sayı: 3
- Basım Tarihi: 2011
- Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.203-211
- Anahtar Kelimeler: Monge-Ampere equation, polynomial, convex surface
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
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.