Topological degree method for the rotationally symmetric $L_p$-Minkowski problem

Jian  Lu; Huaiyu Jian

doi:10.3934/dcds.2016.36.971

Article Contents

2016, Volume 36, Issue 2: 971-980. Doi: 10.3934/dcds.2016.36.971

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Topological degree method for the rotationally symmetric $L_p$-Minkowski problem

Jian Lu^1, and
Huaiyu Jian^2,

1.
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023
2.
Department of Mathematical Sciences, Tsinghua University, Beijing 100084

Received: October 2014

Revised: February 2015

Published: May 2017

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Abstract

Consider the existence of rotationally symmetric solutions to the $L_p$-Minkowski problem for $p=-n-1$. Recently a sufficient condition was obtained for the existence via the variational method and a blow-up analysis in [16]. In this paper we use a topological degree method to prove the same existence and show the result holds under a similar complementary sufficient condition. Moreover, by this degree method, we obtain the existence result in a perturbation case.

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Mathematics Subject Classification: Primary: 35J96, 35J75, 53A15; Secondary: 34C40.

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