The Neumann problem for some degenerate elliptic equations

被引：0
作者：
Cavalheiro A.C. [1 ]
机构：
[1] Department of Mathematics, State University of Londrina
来源：
Applications of Mathematics | 2006年 / 51卷 / 06期
关键词：
degenerate elliptic equations; Neumann problem;
D O I：
10.1007/s10492-006-0025-7
中图分类号：
学科分类号：
摘要：
In the paper we study the equation L u = f, where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set ω. We prove existence and uniqueness of solutions in the space H(ω) for the Neumann problem. © 2006 Mathematical Institute, Academy of Sciences of Czech Republic.
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页码：619 / 628
页数：9
相关论文
共 11 条
[1]  
Chanillo S., Wheeden R.L., Harnack's inequalities and mean-value inequalities for solutions of degenerate elliptic equations, Commun. PDE, 11, pp. 1111-1134, (1986)
[2]  
Chanillo S., Wheeden R.L., Existence and estimates for Green's function for degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa IV Ser. 15, Fasc. II, pp. 309-340, (1988)
[3]  
Franchi B., Serapioni R., Pointwise estimates for a class of strongly degenerate elliptic operators: A geometrical approach, Ann. Sc. Norm. Sup. Pisa C1 Ser. 14, pp. 527-568, (1987)
[4]  
Muckenhoupt B., Weighted norm inequalities for the Hardy maximal function, Trans. Am. Math. Soc., 165, pp. 207-226, (1972)
[5]  
Torchinsky A., Real-Variable Methods in Harmonic Analysis, (1986)
[6]  
Kufner A., John O., Fucik S., Function Spaces, (1977)
[7]  
Kufner A., Weighted Sobolev Spaces, (1985)
[8]  
Heinonen J., Kilpelainen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations Oxford Math. Monographs, (1993)
[9]  
Garcia-Cuerva J., Rubio De Francia J.L., Weighted Norm Inequalities and Related Topics North-Holland Mathematics Studies, 116, (1985)
[10]  
Turesson B.O., Nonlinear Potential Theory and Weighted Sobolev Spaces Lectures Notes in Mathematics, 1736, (2000)
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