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.

引用

页数：21

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