On a Certain Functional Equation and Its Application to the Schwarz Problem

被引：1

作者：

Nikolaev, Vladimir ^{[1
]}

Vasilyev, Vladimir ^{[2
]}

机构：

[1] Yaroslav Wise Novgorod State Univ, Bolshaya St Peterburgskaya Ul 41, Velikiy Novgorod 173003, Russia

[2] Belgorod State Natl Res Univ, Ctr Appl Math, Pobedy St 85, Belgorod 308015, Russia

来源：

MATHEMATICS | 2023年 / 11卷 / 12期

关键词：

J-analytic functions; & lambda; -holomorphic functions; matrix eigenvalue; ellipse; functional equation;

D O I：

10.3390/math11122789

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Schwarz problem for J-analytic functions in an ellipse is considered. In this case, the matrix J is assumed to be two-dimensional with different eigenvalues located above the real axis. The Schwarz problem is reduced to an equivalent boundary value problem for the scalar functional equation depending on the real parameter l. This parameter is determined by the Jordan basis of the matrix J. An analysis of the functional equation was performed. It is shown that for l & ISIN; [0, 1], the solution of the Schwarz problem with matrix J exists uniquely in the Holder classes in an arbitrary ellipse.

引用

页数：10

共 17 条

[11]

Soldatov A.P., 2011, J MATH SCI-U TOKYO, V173, P221, DOI [10.1007/s10958-011-0244-7, DOI 10.1007/S10958-011-0244-7]

[12]

Soldatov A.P., 1989, RUSS DIFFER URAVN, V25, P136

[13]

Soldatov A.P., 2016, DOUGLIS ANAL FUNCTIO

[14] Schwarz Problem for First-Order Elliptic Systems on the Plane [J].

Vasil'ev, V. B. ;

Nikolaev, V. G. .

DIFFERENTIAL EQUATIONS, 2017, 53 (10) :1318-1328

[15]

Vekua I. N., 1967, New Methods for Solving Elliptic Equations

[16] HYPERHOLOMORPHIC FUNCTIONS AND HIGHER-ORDER PARTIAL-DIFFERENTIAL EQUATIONS IN THE PLANE [J].

YEH, RZ .

PACIFIC JOURNAL OF MATHEMATICS, 1990, 142 (02) :379-399

[17]

Zhura N., 1994, DOKL MATH, V48, P142

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