A Calabi theorem for solutions to the parabolic Monge-Ampere equation with periodic data

作者：Zhang, Wei; Bao, Jiguang^*

来源：ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35(5): 1143-1173.

DOI：10.1016/j.anihpc.2017.09.007

• JORGENS
• EXTENSION
• PROPERTY
• MAXIMUM

We classify all solutions to
-u(t) det D(2)u = f (x) in R--(n+1),
where f is an element of C-alpha(R-n) is a positive periodic function in x. More precisely, if u is a parabolically convex solution to above equation, then u is the sum of a convex quadratic polynomial in x, a periodic function in x and a linear function of t. It can be viewed as a generalization of the work of Gutierrez and Huang in 1998. And along the line of approach in this paper, we can treat other parabolic Monge-Ampere equations.

• 出版日期2018-8
• 单位北京师范大学