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研究一类具有Neumann边界条件的Hessian商方程，选取合适的辅助函数，利用极值原理与Hessian算子的结构性质，将梯度估计分为三类情形，依次得到边界梯度估计、近边梯度估计与内部梯度估计，最终得到此类Hessian商方程在f依赖于x、Du时解的全局梯度估计。
Abstract：A class of Hessian quotient equations with Neumann boundary conditions is studied.The gradient estimates are divided into boundary gradient estimates,near-boundary gradient estimates and interior gradient estimates by selecting appropriate auxiliary functions and utilizing maximum principle and structural properties of the Hessian operator.Finally,aglobal gradient estimate for the solutions of such Hessian quotient equations when fdepends on xand Duis obtained.
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基本信息:
DOI：10.13486/j.issn.2097-4973.2026.02.014
中图分类号:O175.25
引用信息:
[1]袁胜通,吴婷婷,韩菲.Hessian商方程Neumann问题解的梯度估计[J].山东航空学院学报,2026,43(02):116-124.DOI:10.13486/j.issn.2097-4973.2026.02.014.
基金信息:
国家自然科学基金项目（12061078）; 新疆维吾尔自治区自然科学基金项目（2024DO1A90）
2026-04-15
2026-04-15