A flow method for a generalization of $ L_{p} $ Christofell-Minkowski problem

Boya Li; Hongjie Ju; Yannan Liu

doi:10.3934/cpaa.2021198

Article Contents

2022, Volume 21, Issue 3: 785-796. Doi: 10.3934/cpaa.2021198

This issue Previous Article Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations Next Article Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities

A flow method for a generalization of $ L_{p} $ Christofell-Minkowski problem

1.
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
2.
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

^*Corresponding author
^*Corresponding author

Received: June 30, 2021

Revised: September 30, 2021

Early access: December 2021

Published: March 2022

This work was supported in part by the Natural Science Foundation of Beijing Municipality (No. 1212002) and the National Natural Science Foundation of China (Grant Nos. 12071017, 11871432, 11871102)

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Abstract

In this paper, a generalitzation of the $ L_{p} $-Christoffel-Minkowski problem is studied. We consider an anisotropic curvature flow and derive the long-time existence of the flow. Then under some initial data, we obtain the existence of smooth solutions to this problem for $ c = 1 $.

Keywords:

$ L_{p} $-Christoffel-Minkowski problem,
existence of solutions,
anisotropic curvature flow.

Mathematics Subject Classification: Primary: 35J96, 35J75; Secondary: 53A15, 53A07.

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References

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