A Bernstein type theorem for parabolic k-Hessian equations. (April 2015) - Nakamori, Saori; Takimoto, Kazuhiro
Abstract: We are concerned with the characterization of entire solutions to the parabolic k -Hessian equation of the form − u t F k ( D 2 u ) = 1 in R n × ( − ∞, 0 ] . We prove that for 1 ≤ k ≤ n, any strictly convex–monotone solution u = u ( x, t ) ∈ C 4, 2 ( R n × ( − ∞, 0 ] ) to − u t F k ( D 2 u ) = 1 in R n × ( − ∞, 0 ] must be a linear function of t plus a quadratic polynomial of x, under some growth assumptions on u .