| 椭圆型方程的边界正则性与Dini条件 |
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| 引用本文： | 邹雄,陈亚浙. 椭圆型方程的边界正则性与Dini条件[J]. 数学学报, 2002, 45(4): 701-710. DOI: cnki:ISSN:0583-1431.0.2002-04-011 |
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| 作者姓名： | 邹雄 陈亚浙 |
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| 作者单位： | 1. 中国科学院数学与系统科学研究院数学所中德合作伙伴小组,北京,100080
2. 北京大学数学科学学院,北京,100871 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 笔者利用Caffarelli扰动方法,证明了Poisson方程和完全非线性一致椭圆型方程在Dini条件下其粘性解的边界正则性,从而给出了文[8]定理4.11不用位势理论的简化证明.
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| 关 键 词： | Poisson方程 完全非线性一致椭圆型方程 粘性解 Dini条件 边界正则性 |
| 文章编号： | 0583-1431(2002)04-0701-10 |
| 修稿时间： | 2001-03-07 |
Boundary Regularity for Elliptic Equations and the Dini Condition |
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| Xiong ZOU. Boundary Regularity for Elliptic Equations and the Dini Condition[J]. Acta Mathematica Sinica, 2002, 45(4): 701-710. DOI: cnki:ISSN:0583-1431.0.2002-04-011 |
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| Authors: | Xiong ZOU |
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| Affiliation: | Xiong ZOU(Partner Group of MPI for Math. in Leipzig at AMSS, Institute of Mathematics, CAS, Beijing 100080, P. R. China)Ya Zhe CHEN (School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China) |
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| Abstract: | Boundary regularity results for viscosity solutions of Poisson's equation and fully nonlinear uniformly elliptic equations under the Dini condition are obtained by use of Caffarelli's perturbation method, which give a simple proof of Theorem 4.11 in [8] without use of potential theory. |
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| Keywords: | Poisson's equation Fully nonlinear uniformly elliptic equations Viscosity solutions Dini condition Boundary regularity |
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