A Bernstein type theorem for parabolic k-Hessian equations. (April 2015)

• Record Type: Journal Article
• Authors: Nakamori, Saori; Takimoto, Kazuhiro
• Is Part Of: Nonlinear analysis. Volume 117(2015)
• Page Start: 211
• Page End: 220
• Publication Date: 2015-04
• Subjects: 35K55 -- 35B08 -- 35K96; Bernstein type theorem -- Fully nonlinear equation -- Parabolic Hessian equation -- Pogorelov type lemma; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.01.010
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .