Violation of unique solvability of the Dirichlet problem on the disk for systems of second-order differential equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Violation of unique solvability of the Dirichlet problem on the disk for systems of second-order differential equations

Authors:

V. P. Burskii

Affiliation:

(1) Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk

Abstract:

We study the Dirichlet problem for the system of elliptic equations with matrix complex-valued coefficients

$au_{x_1 x_1 }^ {text{ + }}bu_{x_1 x_2 }^ {text{ + }}cu_{x_1 x_1 }^ {text{ = 0, }}x in K,{text{ }}u|partial K{text{ }} = 0$

We are concerned with the case in which this homogeneous system of equations can have a countable number of linearly independent solutions. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 23–27, January, 1999.

Keywords:

Dirichlet problem on the disk elliptic differential equation vector-polynomial solution Sobolev space of vector functions

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