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

This article concerns the Minkowski problem for -capacity. We consider the case and 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 . We also provide a proof for...

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Bibliographic Details
Published inAdvanced nonlinear studies Vol. 23; no. 1; pp. 1 - 128
Main Authors Liu, Xinying, Sheng, Weimin
Format Journal Article
LanguageEnglish
Published De Gruyter 11.01.2023
Subjects
35K96
53E99
capacity
curvature flow
Minkowski-type problem
q-capacity
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Summary:This article concerns the Minkowski problem for -capacity. We consider the case and 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 . We also provide a proof for the weak solution to the problem when , which has been obtained by Zou and Xiong.
ISSN:2169-0375
DOI:10.1515/ans-2022-0040