| Sobolev—Lieb—Thirring不等式的推广及其在非自治无穷维动力系统中的应用 |
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| 引用本文： | 殷朝阳,丁伟. Sobolev—Lieb—Thirring不等式的推广及其在非自治无穷维动力系统中的应用[J]. 中山大学学报(自然科学版), 2001, 40(4): 24-27 |
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| 作者姓名： | 殷朝阳 丁伟 |
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| 作者单位： | 1. 中山大学数学系
2. 中山大学物理系 |
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| 基金项目： | 国家自然科学基金资助项目(19871094);广东省自然科学基金资助项目(990229);香港中山大学高等学术中心基金会资助项目(01M5) |
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| 摘 要： | 将在自治的无穷维动力系统吸引子的维数估计中发挥重要技术作用的Sobolev-Lieb-Thirring不等式的适用范围由Banach空间中的单位球面推广到了整个单位球内，使之在非自治无穷维动力系统的吸引子的维数估计中发挥着同样重要的技术作用。
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| 关 键 词： | Sobolev－Lieb－Thirring 吸引子 分形维数估计 非自治无穷维动力系统 Banach空间 偏微分方程 |
| 文章编号： | 0529-6579(2001)04-0024-04 |
| 修稿时间： | 2000-10-13 |
Generalization of the Sololev-Lieb-Thirring Inequality and Its Application in Nonautonomous Infinite Dynamical System |
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| YIN Zhao-yang,DING Wei. Generalization of the Sololev-Lieb-Thirring Inequality and Its Application in Nonautonomous Infinite Dynamical System[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2001, 40(4): 24-27 |
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| Authors: | YIN Zhao-yang DING Wei |
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| Abstract: | The Sobolev-Lieb-Thirring Inequality, which is very important to the dimension estimate of the attractor of an autonomous infinite dimensional system, is generalized from the unit spheral surface to the unit ball of a Banach space, which also plays a key role in the dimension estimate of the attractor of a nonautonomous infinite dimensional system. |
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| Keywords: | Sobolev-Lieb-Thirring inequality dimension estimate of the attractor nonautonomous infinite dynamical system |
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