| Hessian型方程Neumann边值问题的梯度估计 |
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| 引用本文： | 向妮,石菊花,吴燕,刘海蓉. Hessian型方程Neumann边值问题的梯度估计[J]. 数学年刊A辑(中文版), 2017, 38(2): 145-158 |
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| 作者姓名： | 向妮 石菊花 吴燕 刘海蓉 |
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| 作者单位： | 湖北大学数学与统计学学院, 应用数学湖北省重点实验室, 武汉 430062.,湖北大学数学与统计学学院, 应用数学湖北省重点实验室, 武汉 430062.,湖北大学数学与统计学学院, 应用数学湖北省重点实验室, 武汉 430062.,南京林业大学理学院应用数学系, 南京 210037. |
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| 基金项目： | 本文受到国家自然科学基金(No.11101132,No.11401310),湖北省教育厅科学技术研究项目(No.Q20120105),创新思维导向的微分方程课程开放式实践教学体系的研究项目,江苏省自然科学基金(No.BK20140965),江苏省高校自然科学基金(No.14KJB110010)和南京林业大学高层次人才科研基金项目(No.G2014022)的资助. |
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| 摘 要： | 通过构造辅助函数,利用基本对称函数的性质以及函数在极大值点的性质,得到Hessian型方程S_k(D~2u-A(x,u,Du))=B(x,u)的梯度内估计,构造不同的辅助函数,分近边、边界和内部3种情形讨论该方程Neumann边值问题,进而得到全局梯度估计.
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| 关 键 词： | Hessian type equations Neumann boundary value problem Gradient estimates |
| 收稿时间： | 2015-10-12 |
| 修稿时间： | 2016-02-28 |
The Gradient Estimates of Hessian Type Equations for Neumann Boundary Value Problem |
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| XIANG Ni,SHI Juhu,WU Yan and LIU Hairong. The Gradient Estimates of Hessian Type Equations for Neumann Boundary Value Problem[J]. Chinese Annals of Mathematics, 2017, 38(2): 145-158 |
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| Authors: | XIANG Ni SHI Juhu WU Yan LIU Hairong |
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| Affiliation: | Hubei Key Laboratory of Applied Mathmatics, Faculty of Mathematics and Statistics,Hubei University, Wuhan 430062, China.,Hubei Key Laboratory of Applied Mathmatics, Faculty of Mathematics and Statistics,Hubei University, Wuhan 430062, China.,Hubei Key Laboratory of Applied Mathmatics, Faculty of Mathematics and Statistics,Hubei University, Wuhan 430062, China. and College of Science Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China. |
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| Abstract: | In the paper, according to the property of elementary symmetric function and the property ofthe maximum value point, gradient inner estimates of Hessian type equations$S_{k}(D^{2}u-A(x,u,Du))=B(x,u)$ are obtained by the method of auxiliary functions. Then,by constructing different auxiliary functions, the authors study the global gradient estimates of theHessian type equations for Neumann boundary value problem for three different situations:Boundary, near the boundary and inner. |
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| Keywords: | Hessian type equations Neumann boundary value problem Gradient estimates |
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