Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(1): 53-69

Online first article November 25, 2021      Printed January 1, 2022

https://doi.org/10.4134/JKMS.j200665

Copyright © The Korean Mathematical Society.

The interior gradient estimate for a class of mixed Hessian curvature equations

Jundong Zhou

Fuyang Normal University

Abstract

In this paper, we are concerned with a class of mixed Hessian curvature equations with non-degeneration. By using the maximum principle and constructing an auxiliary function, we obtain the interior gradient estimate of $(k-1)$-admissible solutions.

Keywords: Interior gradient, curvature equation, $(k-1)$-admissible solution

MSC numbers: Primary 35J60; Secondary 35B45

Supported by: Research of the author was supported by National Natural Science Foundation of China (grant no.11971253), the Natural Science Foundation of Anhui Province Education Department (grant nos. KJ2017A341 and KJ2018A0330) Quality Enginering Project of Anhui Province Education Department (No. 2018jyxm0491, 2019mooc205, 2020szsfkc0686); Science Research Project of Fuyang Normal University (No. 2021KYQD0011).

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