On some properties of solutions of quasilinear degenerate equations

被引:0
作者
F. I. Mamedov
R. A. Amanov
机构
[1] Azerbaijan National Academy of Sciences,Institute of Mathematics and Mechanics
来源
Ukrainian Mathematical Journal | 2008年 / 60卷
关键词
Elliptic Equation; Boundary Point; Limit Point; Harnack Inequality; Weighted Sobolev Space;
D O I
暂无
中图分类号
学科分类号
摘要
For quasilinear equations div A(x, u, ∇u) = 0 with degeneracy ω(x) of the Muckenhoupt Ap-class, we prove the Harnack inequality, an estimate for the Hölder norm, and a sufficient criterion for the regularity of boundary points of the Wiener type.
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页码:1073 / 1098
页数:25
相关论文
共 20 条
[1]  
Littman W.(1963)Regular points for equations with discontinuous coefficients Ann. Sci. Norm. Super. Pisa Cl. Sci. 17 43-77
[2]  
Stampacchia G.(1982)The local regularity of solutions of degenerate elliptic equations Commun. Part. Different. Equat. 7 77-116
[3]  
Weinherger H. F.(1982)The Wiener test degenerate elliptic equations Ann. Inst. Fourier (Grenoble) 32 151-182
[4]  
Fabes E. B.(1986)Harnack's inequality and mean-value inequalities for solutions of degenerated elliptic equations Commun. Part. Different. Equat. 11 1111-1134
[5]  
Kenig C. E.(1977)A regularity condition at the boundary for solutions of quasilinear elliptic equations Arch. Ration. Mech. Anal. 67 25-39
[6]  
Serapioni R. P.(1997)Smooth approximation in weighted Sobolev spaces Comment. Math. Univ. Carol. 38 29-35
[7]  
Fabes E. B.(1997)Approximation and embedding theorems for weighted Sobolev spaces associated with Lipschitz continuous vector fields Boll. Unione Mat. Ital. 7 83-117
[8]  
Jersion D.(1992)Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces Amer. J. Math. 114 813-874
[9]  
Kenig C.(1963)On some problems in the qualitative theory of elliptic equations Usp. Mat. Nauk 18 3-62
[10]  
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