Dirichlet problem with degeneration of the input data on the boundary of the domain

被引：3

作者：

Rukavishnikov, V. A. ^{[1
]}

Rukavishnikova, E. I. ^{[1
]}

机构：

[1] Russian Acad Sci, Far Eastern Branch, Ctr Comp, Khabarovsk, Russia

来源：

DIFFERENTIAL EQUATIONS | 2016年 / 52卷 / 05期

关键词：

FINITE-ELEMENT-METHOD; SINGULARITY; EQUATIONS;

D O I：

10.1134/S0012266116050141

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define an R-v-generalized solution of the first boundary value problem for a second-order elliptic equation with degeneration of the input data on the entire boundary of the two-dimensional domain and prove the existence and uniqueness of the solution in the weighted set (W)over dot(2,v) (vertical bar) (1)(beta/2) (Omega,delta).

引用

页码：681 / 685

页数：5

共 11 条

[1]

Aubin J.P.., 1972, APPROXIMATION ELLIPT

[2]

LIZORKIN PI, 1981, DOKL AKAD NAUK SSSR+, V259, P28

[3]

LIZORKIN PI, 1981, DOKL AKAD NAUK SSSR+, V257, P278

[4]

Nikol'skii S.M., 1979, T MIAN, V150, P212

[5] On the isomorphic mapping of weighted spaces by an elliptic operator with degeneration on the domain boundary [J].

Rukavishnikov, V. A. ;

Rukavishnikova, E. I. .

DIFFERENTIAL EQUATIONS, 2014, 50 (03) :345-351

[6] Weighted finite element method for an elasticity problem with singularity [J].

Rukavishnikov, V. A. ;

Nikolaev, S. G. .

DOKLADY MATHEMATICS, 2013, 88 (03) :705-709

[7] ON THE ERROR ESTIMATION OF THE FINITE ELEMENT METHOD FOR THE BOUNDARY VALUE PROBLEMS WITH SINGULARITY IN THE LEBESGUE WEIGHTED SPACE [J].

Rukavishnikov, V. A. ;

Rukavishnikova, H. I. .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2013, 34 (12) :1328-1347

[8] The finite element method for a boundary value problem with strong singularity [J].

Rukavishnikov, V. A. ;

Rukavishnikova, H. I. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (09) :2870-2882

[9] On the coercivity of the Rv-generalized solution of the first boundary value problem with coordinated degeneration of the input data [J].

Rukavishnikov, VA ;

Ereklintsev, AG .

DIFFERENTIAL EQUATIONS, 2005, 41 (12) :1757-1767

[10] New numerical method for solving time-harmonic Maxwell equations with strong singularity [J].

Rukavishnikov, Victor A. ;

Mosolapov, Andrey O. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (06) :2438-2448

← 1 2 →