| 各项异性椭圆方程基本解的存在性 |
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| 引用本文： | 吕小敏,魏公明.各项异性椭圆方程基本解的存在性[J].纯粹数学与应用数学,2016,32(4):362-379. |
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| 作者姓名： | 吕小敏 魏公明 |
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| 作者单位： | 上海理工大学理学院,上海,200093;上海理工大学理学院,上海,200093 |
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| 基金项目： | 沪江基金(B14005) |
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| 摘 要： | 证明了右端可测的各项异性椭圆方程基本解的存在性,其中应用了各项异性Sobolev空间和Lebesgue空间.首先得到近似方程的解,然后通过对这些解的子列取极限,得到原方程的解.关键是要有一个近似函数空间以及近似方程的先验估计.最后运用Vitali定理证明了原方程基本解的存在性,推广和改进了已有方程.
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| 关 键 词： | 各项异性方程 弱解 格林函数 Vitali定理 基本解 |
The existence of fundamental solution for anisotropic elliptic equation |
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| L¨u Xiaomin,Wei Gongming.The existence of fundamental solution for anisotropic elliptic equation[J].Pure and Applied Mathematics,2016,32(4):362-379. |
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| Authors: | L¨u Xiaomin Wei Gongming |
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| Abstract: | This paper proves the existence of fundamental solution for anisotropic equation??p?u??q?u=δ0 with measure valued right hand-side.Anisotropic Sobolev space and weak Lebesgue space are involved in the functional setting.First,we get the solutions of approximate equations.Then by taking limit of the sequence of these solutions,we get the solution of the original equation.The point is to have a approximate function space and do a priori estimate for the approximate equations.Final,the Vitali’s theorem is applied for the existence of funda-mental solution for anisotropic equation??p?u??q?u=δ0.Extend and improve the existing equation??p?u=δ0. |
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| Keywords: | anisotropic equations weak solution Green’s function Vitali’s convergence theorem fundamental solution |
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