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作者(中文):牟柏丞
作者(外文):Mou, Po-Cheng
論文名稱(中文):流形上的非線性拉普拉斯算子之梯度估計
論文名稱(外文):A note on gradient estimate for p-Laplacian on complete manifolds
指導教授(中文):宋瓊珠
指導教授(外文):Sung, Chiung-Jue
口試委員(中文):高淑蓉
王嘉平
口試委員(外文):Kao, Shu-Jung
Wang, Jia-Ping
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學號:103021616
出版年(民國):106
畢業學年度:105
語文別:英文
論文頁數:40
中文關鍵詞:流形拉普拉斯梯度估計
外文關鍵詞:manifoldLaplaciangradient estimate
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  在本篇論文中,我們研究在完備流形上非線性拉普拉斯算子的梯度估計,並研究當主特徵根達到最大值時,流形的頻譜分析。

In this papar, we study the gradient estimate for p-Laplacian on complete manifolds with Ricci curvature bounded from below. We also study the bottom spectrum when the first eigenvalue of the p-Laplacian achieves its maximum.
1. Introduction 2
2. Preliminary 3
3. Gradient Estimate for p-Laplacian 8
3.1. Gradient Estimate for Eigenfunction 8
3.2. Proof of Main Theorem 14
4. Splitting Theorem 28
4.1. Splitting Theorem for Laplacian 29
4.2. Splitting Theorem for p-Laplacian 34
References 39
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[10] P. Li and J. Wang, Weighted Poincare inequality and rigidity of complete manifolds, Ann.
Sci. Ecole. Norm. Sup. (4) 39 (2006), 921-982
[11] L. Salo -Coste, Uniformly elliptic operators on Riemannian manifolds, J. Di erential Geom.
36 (1992), no. 2, 417-450
[12] R. Schoen and S. T. Yau, Lectures on Di erential Geometry, International Press, Boston,
(1994)
[13] C. J. Sung and J.Wang, Sharp gradient estimate and spectral rigidity for p-Laplacian, Math.
Res. Lett. 21 (2014), no. 4, 885-904
[14] X. Wang and L. Zhang, Local gradient estimate for p-harmonic functions on Riemannian
manifolds, Comm. Anal. Geom. 19 (2011), 759{772
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28 (1975), 201-228
 
 
 
 
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