Multiple solutions of the Lp -Minkowski problem

Yan He; Qi Rui Li; Xu Jia Wang

doi:10.1007/s00526-016-1063-y

Multiple solutions of the L_p -Minkowski problem

Yan He, Qi Rui Li, Xu Jia Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

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 Sⁿ 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 , 1} solutions.

Original language	English
Article number	117
Journal	Calculus of Variations and Partial Differential Equations
Volume	55
Issue number	5
DOIs	https://doi.org/10.1007/s00526-016-1063-y
Publication status	Published - 1 Oct 2016

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abstract = "In this paper, we study the existence of multiple solutions to the Lp-Minkowski problem. We prove if p< - n, then for any integer N> 0 , there exists a smooth positive function f on Sn such that the Lp-Minkowski problem admits at least N different smooth solutions. We also construct nonsmooth, positive function f for which the Lp-Minkowski problem has infinitely many C1 , 1 solutions.",

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Multiple solutions of the L_p -Minkowski problem

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