| Unique Continuation on Quadratic Curves for Harmonic Functions |
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| 作者姓名： | Yufei KE Yu CHEN |
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| 作者单位： | School of Mathematics |
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| 基金项目： | This work was supported by the National Natural Science Foundation of China(No.11971121). |
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| 摘 要： | The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated. The numerical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.
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| 关 键 词： | Unique continuation Quadratic curves Harmonic function |
| 收稿时间： | 2021/3/15 0:00:00 |
| 修稿时间： | 2021/10/21 0:00:00 |
Unique Continuation on Quadratic Curves for Harmonic Functions* |
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| Yufei KE,Yu CHEN.Unique Continuation on Quadratic Curves for Harmonic Functions[J].Chinese Annals of Mathematics,Series B,2022,43(1):17-32. |
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| Authors: | Yufei KE Yu CHEN |
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| Institution: | School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China.; Corresponding author. School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China. |
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| Abstract: | The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated. The numerical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively. |
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| Keywords: | Unique continuation Quadratic curves Harmonic function |
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