退化Hessian商方程Neumann问题的梯度估计
Gradient Estimates on Degenerate Hessian Equations with Neumann Problem
DOI: 10.12677/pm.2024.149327, PDF,    国家自然科学基金支持
作者: 孙文静*, 韩 菲#, 武春雨：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 退化Hessian商方程；Neumann问题；梯度估计；Degenerate Hessian Quotient Equations； Neumann Problem； Gradient Estimates
摘要: 研究一类退化Hessian商方程Neumann问题，通过选取恰当的辅助函数，利用极大值原理和基本对称函数的性质，在条件 f 1/ k−l ∈ C 1 ( Ω ¯ × ℝ n ) 下得到该方程当 f 依赖于 x,Du 时解的全局梯度估计。
Abstract: In this paper, degenerate Hessian quotient equations with Neumann problem has studied. By choosing suitable auxiliary functions, using the maximum principle and the properties of basic symmetric functions, with the f 1/ k−l ∈ C 1 ( Ω ¯ × ℝ n ) condition, the global gradient estimation for the admissible solution of the equations with dependent on x and Du has obtained.
文章引用：孙文静, 韩菲, 武春雨. 退化Hessian商方程Neumann问题的梯度估计[J]. 理论数学, 2024, 14(9): 61-66. https://doi.org/10.12677/pm.2024.149327

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