| 一类Sobolev空间范数的等价性证明 |
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| 引用本文： | 杨丽萍. 一类Sobolev空间范数的等价性证明[J]. 安庆师范学院学报(自然科学版), 2008, 14(4) |
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| 作者姓名： | 杨丽萍 |
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| 作者单位： | 南京理工大学理学院应用数学系,江苏南京,210094 |
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| 摘 要： | Sobolev空间已成为现代偏微分方程理论研究的重要工具。可利用插值不等式证明一般的Sobolev空间中范数的等价性,并通过构造高阶椭圆型方程的边值问题,利用边值问题的可解性及正则性,得到一类带有边界条件限制的Sobolev空间范数的等价性。
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| 关 键 词： | Sobolev空间 范数 擂值不等式 正则性理论 |
Proof on the Equivalence of Norms for a Class of Sobolev Spaces |
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| YANG Li-ping. Proof on the Equivalence of Norms for a Class of Sobolev Spaces[J]. Journal of Anqing Teachers College(Natural Science Edition), 2008, 14(4) |
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| Authors: | YANG Li-ping |
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| Affiliation: | YANG Li-ping(Department of Applied Mathematics,Nanjing University of Science & Technology,Nanjing 210094,China) |
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| Abstract: | The Sobolev space has been an important tool to study modern theory of partial differential equations.In this paper,the author proves the equivalence of norms in generic Sobolec spaces by using interpolation inequalities.In addition,the equivalence of norms in a class of Sobolev spaces is established by constructing the boundary value problems of corresponding higher order elliptic equations,and using the solvability and regularity of the boundary value problems. |
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| Keywords: | Sobolev spaces norms interpolation inequality regularity theory |
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