A Constant Rank Theorem for Quasiconcave Solutions of Fully Nonlinear Partial Differential Equations

作者：Bian, Baojun^*; Guan, Pengfei; Ma, Xi-Nan; Xu, Lu

来源：Indiana University Mathematics Journal, 2011, 60(1): 101-119.

DOI：10.1512/iumj.2011.60.4222

• level set convexity
• fully nonlinear equations

We prove a constant rank theorem for the second fundamental form of the convex level surfaces of solutions to equations F (D(2)u, Du, u, x) = 0 under a structural condition introduced by Bianchini-Longinetti-Salani in [2].

• 单位
  同济大学; 中国科学技术大学; 中国科学院武汉物理与数学研究所