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

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI:10.1515/ans-2022-0040

Xinying Liu, Weimin Sheng

引用次数: 1

Abstract

Abstract This article concerns the L p {L}_{p} Minkowski problem for q-capacity. We consider the case p ≥ 1 p\ge 1 and 1 < q < n 1\lt q\lt n in the smooth category by a kind of curvature flow, which converges smoothly to the solution of a Monge-Ampére type equation. We show the existence of smooth solution to the problem for p ≥ n p\ge n . We also provide a proof for the weak solution to the problem when p ≥ 1 p\ge 1 , which has been obtained by Zou and Xiong.

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Lp-Minkowski型q容量问题的曲率流

研究q-capacity的L p {L}_{p} Minkowski问题。考虑一类曲率流在光滑范畴中p≥1 p\ge 1和1 < q < n 1\lt q\lt n的情况，该情况平滑地收敛于一个monge - ampsamre型方程的解。我们证明了p≥n p\ge n时问题光滑解的存在性。我们也证明了当p≥1 p\ge 1时问题的弱解，这是邹和熊已经得到的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.