A curvature flow to the Lp Minkowski-type problem of q-capacity

被引：1
|
作者：
Liu, Xinying [1 ]
Sheng, Weimin [1 ]
机构：
[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China
来源：
ADVANCED NONLINEAR STUDIES | 2023年 / 23卷 / 01期
基金：
中国国家自然科学基金;
关键词：
q-capacity; Minkowski-type problem; curvature flow; INEQUALITY; HYPERSURFACES;
D O I：
10.1515/ans-2022-0040
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article concerns the Lp Minkowski problem for q-capacity. We consider the case p >= 1 and 1 < q < nin the smooth category by a kind of curvature flow, which converges smoothly to the solution of a Monge-Amp & eacute;re type equation. We show the existence of smooth solution to the problem for p >= n. We also provide a proof for the weak solution to the problem when p >= 1, which has been obtained by Zou and Xiong.
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页数：21
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