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| 加权流形上加权p-Laplace特征值问题的第一特征值下界估计 | |
| 引用本文： | 张留伟,赵艳. 加权流形上加权p-Laplace特征值问题的第一特征值下界估计[J]. 数学杂志, 2016, 36(2): 277-284 |
| 作者姓名： | 张留伟 赵艳 |
| 作者单位： | 同济大学数学系, 上海 200092;信阳师范学院数学系, 河南 信阳 464000,大连理工大学数学科学学院, 辽宁 大连 116024;河南轻工业学校公共课数学部, 河南 郑州 450000 |
| 基金项目： | Supported by National Natural Science Foundation of China (11201400) |
| 摘 要： | 本文研究了加权流形上加权p-Laplacian特征值问题的第一特征值下界估计的问题.利用余面积公式、Cavalieri原理以及Federer-Fleming定理,获得了由Cheeger常数或等周常数确定的第一特征值的下界估计. |
| 关 键 词： | 加权p-Laplacian 加权流形 等周常数 第一特征值 下界 |
| 收稿时间： | 2015-04-13 |
| 修稿时间： | 2015-07-06 |
ISOPERIMETRIC ESTIMATE OF THE FIRST EIGENVALUES FOR THE WEIGHTED p-LAPLACIAN ON MANIFOLDS |
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| ZHANG Liu-wei and ZHAO Yan. ISOPERIMETRIC ESTIMATE OF THE FIRST EIGENVALUES FOR THE WEIGHTED p-LAPLACIAN ON MANIFOLDS[J]. Journal of Mathematics, 2016, 36(2): 277-284 | |
| Authors: | ZHANG Liu-wei and ZHAO Yan |
| Affiliation: | Department of Mathematics, Tongji University, Shanghai 200092, China;Department of Mathematics, Xinyang Normal University, Xinyang 464000, China and School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;Public Course Teaching Department, Henan Light Industry School, Zhengzhou 450000, China |
| Abstract: | In this paper, we estimate the lower bounds of the first eigenvalues for the weighted p-Laplacian on manifolds. By using the coarea formula, the Cavalieri principle and the FedererFleming theorem, we obtain the estimation of the lower bounds for the first eigenvalues by the Cheeger constant or the isoperimetric constant. |
| Keywords: | weighted p-Laplacian weighted manifold isoperimetric constant first eigenvalue lower bound |
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