Dirichlet type problem for the system of elliptic equations, which order degenerate at a line

被引：2

作者：

Rutkauskas, Stasys ^{[1
]}

机构：

[1] Vilnius Univ, Inst Math & Informat, LT-08663 Vilnius, Lithuania

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2014年 / 19卷 / 03期

关键词：

systems of elliptic equations; degenerating elliptic systems; Dirichlet type problem; ASYMPTOTIC CONDITIONS; POINT;

D O I：

10.15388/NA.2014.3.11

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dirichlet type problem in a bounded domain for the system of linear elliptic equations of second order, which degenerate into first order system at a line crossing the domain, is studied. The existence and uniqueness of a solution of this problem in the Holder class of functions are proved without any additional condition at line of degeneracy. The only requirement is that the solution is bounded in the considered domain.

引用

页码：476 / 487

页数：12

共 50 条

[31] The Dirichlet problem for an elliptic system of an even number of second-order equations
Artem'eva, SV
DIFFERENTIAL EQUATIONS, 2000, 36 (12) : 1872 - 1875
[32] Radial viscosity solutions of the Dirichlet problem for semilinear degenerate elliptic equations
Maruo, K
Tomita, Y
OSAKA JOURNAL OF MATHEMATICS, 2001, 38 (04) : 737 - 757
[33] Estimates of the spectrum of semiperiodical Dirichlet problem for a class of degenerate elliptic equations
Muratbekov, M. B.
Muratbekov, M. M.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (10) : 1131 - 1146
[34] Existence of solutions for the Dirichlet problem of some degenerate semilinear elliptic equations
Cavalheiro, Albo Carlos
APPLIED MATHEMATICS LETTERS, 2010, 23 (03) : 317 - 321
[35] Existence of solutions for Dirichlet problem of some degenerate quasilinear elliptic equations
Cavalheiro, Albo Carlos
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2008, 53 (02) : 185 - 194
[36] Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations
Cavalheiro, Albo Carlos
JOURNAL OF APPLIED ANALYSIS, 2014, 20 (02) : 145 - 154
[37] On the Weak Solvability of Dirichlet Problem for a Fractional Order Degenerate Elliptic Equation
Mamedov, F. I.
Mammadzada, N. M.
Mammadli, S. M.
AZERBAIJAN JOURNAL OF MATHEMATICS, 2024, 14 (01): : 69 - 78
[38] The Dirichlet problem for sub-elliptic second order equations
Parmeggiani A.
Xu C.-J.
Annali di Matematica Pura ed Applicata, 1997, 173 (1) : 233 - 243
[39] THE DIRICHLET PROBLEM FOR SECOND ORDER SEMILINEAR ELLIPTIC AND PARABOLIC EQUATIONS
Tersenov, Alkis
DIFFERENTIAL EQUATIONS & APPLICATIONS, 2009, 1 (03): : 393 - 411
[40] The dirichlet problem for second order elliptic equations with singular data
L. Caso
M. Transirico
Acta Mathematica Hungarica, 1997, 76 : 1 - 16

← 1 2 3 4 5 →