| 一类A-调和方程的障碍问题的很弱解的全局正则性 |
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| 引用本文： | 周树清,胡振华,彭冬云.一类A-调和方程的障碍问题的很弱解的全局正则性[J].数学物理学报(A辑),2014,34(1):27-38. |
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| 作者姓名： | 周树清 胡振华 彭冬云 |
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| 作者单位： | 1.湖南师范大学数学与计算机科学学院 长沙 410081;
2.高性能计算与随机信息处理省部共建教育部重点实验室 长沙 410081;
3.湖南城市学院数学系 湖南益阳 413000 |
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| 基金项目： | 国家自然科学基金(11271120, 10971061)、湖南省自科基金(11JJ6005)、湖南省重点学科建设项目和湖南师范大学青优培养计划(080640)资助. |
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| 摘 要： | 应用Hodge分解定理,得到了非齐次A-调和方程-div(A(x,Du(x)))=f(x,u(x))对应的障碍问题很弱解的局部和全局的W~(1,q)(Ω)-正则性,其中,A(x,Du(x)),f(x,u(x))满足文中所给的条件,从而推广了相关文献中的有关结果.该结果在优化控制问题中有着广泛的应用.
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| 关 键 词： | 非齐次A-调和方程 障碍问题 优化控制 Hodge分解 全局W~( q)(Ω)-正则性. |
| 收稿时间： | 2012-04-08 |
| 修稿时间： | 2013-07-04 |
Global Regularity for Very Weak Solutions to Obstacle Promlems Corresponding to a Class of A-Harmonic Equations |
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| ZHOU Shu-Qing,HU Zhen-Hua,PENG Dong-Yun.Global Regularity for Very Weak Solutions to Obstacle Promlems Corresponding to a Class of A-Harmonic Equations[J].Acta Mathematica Scientia,2014,34(1):27-38. |
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| Authors: | ZHOU Shu-Qing HU Zhen-Hua PENG Dong-Yun |
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| Institution: | 1.School of Mathematics and Computer Science of Hunan Normal University, Changsha 410081;
2.Key Laboratory of High Performance Computing and Stochastic Information Processing, Changsha 410081;
3.Department of Mathematics, Hunan City University, Hunan |Yiyang 413000 |
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| Abstract: | Using Hodge decomposition theorem, the local and the global W1, q(Ω)-regularity results for very weak solutions to the obstacle problems associated with the following non-homogeneous A-harmonic equations
-div(A(x, Du(x)))=f(x, u(x))
are obtained under certain conditions on A(x, Du(x)), f(x, u(x)) listed in the context. The results generalize the corresponding results in related literatures. The results can be widely applied to optimal control problems. |
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| Keywords: | Non-homogeneous A-harmonic equationszz Obstacle problemszz Optimal controlzz Hodge decompositionzz Global W1 q(&Omega )-regularityzz |
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