THE RIEMANN-HILBERT PROBLEM IN A DOMAIN WITH PIECEWISE SMOOTH BOUNDARIES IN WEIGHT CLASSES OF CAUCHY TYPE INTEGRALS WITH A DENSITY FROM VARIABLE EXPONENT LEBESGUE SPACES

被引：0

作者：

Kokilashvili, Vakhtang ^{[1
]}

Paatashvili, Vakhtang ^{[1
]}

机构：

[1] A Razmadze Math Inst, GE-0193 Tbilisi, Georgia

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2009年 / 16卷 / 04期

基金：

美国国家科学基金会;

关键词：

Cauchy type integrals; the Riemann-Hilbert problem; weighted Lebesgue space with variable exponent; Log-Holder condition; piecewise smooth boundary; non Fredholmian case; OPERATORS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Riemann-Hilbert problem for an analytic function is solved in weighted classes of Cauchy type integrals in a simply connected domain not containing z = infinity and having a density from variable exponent Lebesgue spaces. It is assumed that the domain boundary is a piecewise smooth curve. The solvability conditions are established and solutions are constructed. The solution is found to essentially depend on the coefficients from the boundary condition, the weight, space exponent values at the angular points of the boundary curve and also on the angle values. The non-Fredholmian case is investigated. An application of the obtained results to the Neumann problem is given.

引用

页码：737 / 755

页数：19

共 12 条

[1] The Riemann-Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue spaces
Kokilashvili, Vakhtang
Meskhi, Alexander
Paatashvili, Vakhtang
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2016, 170 (02) : 208 - 211
[2] Riemann-Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue Spaces
Kokilashvili, V.
Paatashvili, V.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2018, 63 (09) : 1233 - 1257
[3] The Riemann-Hilbert Problem in Weighted Classes of Cauchy Type Integrals with Density from LP(.)(Γ)
Kokilashvili, Vakhtang
Paatashvili, Vakhtang
COMPLEX ANALYSIS AND OPERATOR THEORY, 2008, 2 (04) : 569 - 591
[4] The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces
Kokilashvili, Vakhtang
Meskhi, Alexander
Paatashvili, Vakhtang
GEORGIAN MATHEMATICAL JOURNAL, 2016, 23 (04) : 551 - 558
[5] The Riemann–Hilbert Problem in Weighted Classes of Cauchy Type Integrals with Density from LP( · )(Γ)
Vakhtang Kokilashvili
Vakhtang Paatashvili
Complex Analysis and Operator Theory, 2008, 2 : 569 - 591
[6] Riemann-Hilbert problem for variable exponent poly-Smirnov space on a piecewise Lyapunov boundary
He, Fuli
Zhou, Xianli
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024, 69 (09) : 1437 - 1461
[7] Integral Representation of Solutions and Riemann-Hilbert Type Problem for the Cauchy-Riemann Equation with Strong Singularity in the Lower Order Coefficient in a Domain with Piecewise Smooth Boundary
Rasulov, A. B.
Yakivchik, N. V.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2024, 64 (11) : 2643 - 2654
[8] Lp;r spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
Huseynli, Ali
Mirzabalayeva, Asmar
SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2019, 16 (01): : 83 - 91
[9] On the Riemann-Hilbert boundary value problem for generalized analytic functions in the framework of variable exponent spaces
Kokilashvili, V.
Paatashvili, V.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (18) : 7267 - 7286
[10] THE RIEMANN PROBLEM AND LINEAR SINGULAR INTEGRAL EQUATIONS WITH MEASURABLE COEFFICIENTS IN LEBESGUE TYPE SPACES WITH A VARIABLE EXPONENT
Paatashvili, Vakhtang
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2014, 61 : 103 - 145

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