Solvability of singular integro-differential equations via Riemann-Hilbert problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Li, Pingrun¹  Ren, Guangbin² 

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

关键词: Singular integro-different equations;    Riemann-Hilbert problem;    Cauchy kernels;    Convolution kernel;   

DOI  :  10.1016/j.jde.2018.07.056

来源: Elsevier

【 摘 要 】

The article is to study singular integro-differential equations involving convolutional operators and Cauchy integral operators via Riemann-Hilbert problem. To do this, we adopt a new approach through Fourier transform on L-2 subspace which is Holder-continuous with a certain decay at infinity. The Fourier transform converts the equations into a Riemann-Hilbert problem with Holder-continuous coefficients and with nodal points, which allows us to construct the general solutions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free