| On the Unique Continuation Properties for Elliptic Operators with Singular Potentials |
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| 引用本文： | Xiang Xing TAO Song Yan ZHANG. On the Unique Continuation Properties for Elliptic Operators with Singular Potentials[J]. 数学学报(英文版), 2007, 23(2): 297-308. DOI: 10.1007/s10114-005-0869-x |
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| 作者姓名： | Xiang Xing TAO Song Yan ZHANG |
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| 作者单位： | Department of Mathematics, Faculty of Science, Ningbo University, Ningbo 315211, P. R. China |
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| 基金项目： | This work is supported by National Nature of Science Foundation of China （No. 10471069） and by Natural Science Foundation of Zhejiang province of China （No. 102066） and by NSF of Ningbo city （No. 2006A610090） |
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| 摘 要： | Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato-Fefferman-Phong＇s class in Lipschitz domains. An elementary proof of the doubling property for u^2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the Bp weight properties for the solution u near the boundary.
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| 关 键 词： | 椭圆算子 奇异位势 唯一开拓性质 二阶偏微分方程 |
| 修稿时间： | 2004-09-222005-06-07 |
On the Unique Continuation Properties for Elliptic Operators with Singular Potentials |
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| Xiang Xing Tao,Song Yan Zhang. On the Unique Continuation Properties for Elliptic Operators with Singular Potentials[J]. Acta Mathematica Sinica(English Series), 2007, 23(2): 297-308. DOI: 10.1007/s10114-005-0869-x |
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| Authors: | Xiang Xing Tao Song Yan Zhang |
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| Affiliation: | (1) Department of Mathematics, Faculty of Science, Ningbo University, Ningbo 315211, P. R. China |
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| Abstract: | Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato–Fefferman–Phong’s class in Lipschitz domains. An elementary proof of the doubling property for u 2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the ℬ p weight properties for the solution u near the boundary. This work is supported by National Nature of Science Foundation of China (No. 10471069) and by Natural Science Foundation of Zhejiang province of China (No. 102066) and by NSF of Ningbo city (No. 2006A610090) |
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| Keywords: | doubling property unique continuation Lipschitz domain Kato– Fefferman– Phong’ s potential |
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