| THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS |
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| 引用本文： | 赵俊宁 曾小明. THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS[J]. 数学物理学报(B辑英文版), 2005, 25(4): 577-586. DOI: 10.1016/S0252-9602(17)30196-0 |
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| 作者姓名： | 赵俊宁 曾小明 |
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| 作者单位： | Department of Mathematics, Xiamen University, Xiamen 361005, China |
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| 摘 要： | In this paper, the first boundary value problem for quasilinear equation of the form △A（u,x）＋∑i=1^m δb^i（u,x）/δxi＋c（u,x）=0,Au（u,x） ≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.
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| 关 键 词： | 准线性退化椭圆方程 边值问题 弱解 存在性 唯一性 |
| 收稿时间： | 2002-09-02 |
| 修稿时间： | 2003-12-24 |
THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS |
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| Zhao Junning,Zeng Xiaoming. THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS[J]. Acta Mathematica Scientia, 2005, 25(4): 577-586. DOI: 10.1016/S0252-9602(17)30196-0 |
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| Authors: | Zhao Junning Zeng Xiaoming |
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| Affiliation: | 1. Institut für Informationsverarbeitung, Leibniz Universität Hannover, Appelstraße 9a, 30167 Hannover, Germany;2. University of Science and Technology of China, Jinzhai Rd, Hefei, Anhui 230027, China;1. Escola de Engenharia de São Carlos (EESC), Universidade de São Paulo (USP), Av. Trabalhador São-Carlense 400, CEP 13.566-590, São Carlos, SP, Brazil;2. Escola de Engenharia Mauá (EEM), Instituto Mauá de Tecnologia (IMT), Praça Mauá 1, CEP 09.580-900, São Caetano do Sul, SP, Brazil |
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| Abstract: | In this paper, the first boundary value problem for quasilinear equation of the form △A(u, x) m∑i=1(e)bi(u,x)/(e)xi c(u,x)=0,Au(u,x)≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved. |
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| Keywords: | Dirichlet problem degenerate elliptic equation existence of solutions |
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