Multiple solutions of the Lp-Minkowski problem

作者：He, Yan; Li, Qi-Rui; Wang, Xu-Jia^*

来源：Calculus of Variations and Partial Differential Equations, 2016, 55(5): 117.

DOI：10.1007/s00526-016-1063-y

• ANISOTROPIC CURVATURE FLOW
• SIMILAR SHRINKING CURVES
• NONUNIQUENESS
• INEQUALITIES
• EQUATIONS

In this paper, we study the existence of multiple solutions to the L-p-Minkowski problem. We prove if p < -n, then for any integer N > 0, there exists a smooth positive function f on S-n such that the L-p-Minkowski problem admits at least N different smooth solutions. We also construct nonsmooth, positive function f for which the L-p-Minkowski problem has infinitely many C-1,C-1 solutions.

• 出版日期2016-10
• 单位中南大学