Regularity of the solutions of degenerate elliptic equations in divergent form

被引：0
作者：
R. A. Amanov
F. I. Mamedov
机构：
[1] National Academy of Sciences of Azerbaijan,Institute of Mathematics and Mechanics
[2] Dicle University,undefined
来源：
Mathematical Notes | 2008年 / 83卷
关键词：
elliptic equation of divergence form; Dirichlet problem; Lipschitz condition; Lebesgue norm; Lebesgue measure; Hölder’s inequality;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A priori estimates of the solution to the Dirichlet problem and of its first derivatives in terms of weighted Lebesgue norms are obtained for linear and quasilinear equations with degeneracy from Ap Muckenhoupt classes.
引用
收藏
页码：3 / 13
页数：10
相关论文
共 18 条
[1]  
Stampacchia G.(1958)Contributi alla regolarizzazione della soluzioni del problemi al contro per equazi del secondo ordine ellitici Ann. Scuola Norm. Sup. Pisa (3) 12 223-245
[2]  
Chicco M.(1971)An a priori inequality concerning elliptic second-order partial differential equations of variational type Matematiche (Catania) 26 173-182
[3]  
Maz’ya V. G.(1969)On weak solutions of the Dirichlet and Neumann problems Trudy Moskov. Mat. Obshch. 20 137-172
[4]  
Talenti G.(1976)Elliptic equations and rearrangements Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 697-718
[5]  
Mamedov F. I.(1993)Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form,” the regularity of the solutions of the linear and quasilinear equations of elliptic type in the divergent form Mat. Zametki 53 50-58
[6]  
Kilpeläinen W.(1997)Smooth approximation in weighted Sobolev spaces Comment. Math. Univ. Corolin. 38 29-35
[7]  
Littman G.(1963)Regular points for equations with discontinuous coefficients Ann. Scuola Norm. Sup. Pisa (3) 17 43-77
[8]  
Stampacchia H. F.(1982)The local regularity of solutions of degenerate elliptic equations Comm. Partial Differential Equations 7 77-116
[9]  
Weinberger E. B.(1982)The Wiener test for degenerate elliptic equations Ann. Inst. Fourier (Grenoble) 32 151-182
[10]  
Fabes C. E.(1992)Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces Amer. J. Math. 114 813-874
12