| 一类Sobolev空间紧嵌入定理 |
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| 引用本文： | 林振生.一类Sobolev空间紧嵌入定理[J].福建工程学院学报,2021,0(1):81-83. |
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| 作者姓名： | 林振生 |
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| 作者单位： | 福建工程学院计算机科学与数学学院 |
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| 摘 要： | 利用H?lder插值不等式论证了仅需Sobolev空间有界弱收敛子序列在某个Lp(RN)空间上强收敛。借助更弱位势函数自身性质、有界区域上经典的Sobolev紧嵌入定理，巧妙地将全空间划分为3个特殊区间，证明了带有更弱位势函数的一类Sobolev空间紧嵌入定理。有效地解决了带有位势函数的椭圆偏微分方程解的存在性因工作空间失去紧性所产生的困难。
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| 关 键 词： | Sobolev空间 位势函数 H?lder不等式 紧嵌入 |
Imbedding theorem for a kind of Sobolev space |
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| LIN Zhensheng.Imbedding theorem for a kind of Sobolev space[J].Journal of Fujian University of Technology,2021,0(1):81-83. |
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| Authors: | LIN Zhensheng |
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| Institution: | School of Computer Science and Mathematics, Fujian University of Technology |
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| Abstract: | The H?lder interpolating inequality was used to prove that the Sobolev compact imbedding theorem holds if and only if the bounded sequence has some strong converge sequence for some Lp(RN). By the properties of the weaker potential function, the compact imbedding theorem on the bound domain along with three special partitions of the entire space, the compact imbedding theorem was verified for some kind of Sobolev space with weaker potential function. And such a theorem could be useful for the study of the existence of a solution for some type of the elliptic equations which possess this kind of potential function when compactness for the functional space fails. |
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| Keywords: | Sobolev space potential function H?lder inequality compact imbedding |
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