The Riemann-Hilbert problem and the generalized Neumann kernel on multiply connected regions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:214

Article

Wegmann, Rudolf¹  Nasser, Mohamed M. S.² 

[1] Max Planck Inst Astrophys, D-85748 Garching, Germany

[2] Ibb Univ, Fac Sci, Dept Math, Ibb, Yemen

关键词: Riemann-Hilbert problems;    generalized Neumann kernel;    multiply connected regions;    Fredholrn integral equations;   

DOI  :  10.1016/j.cam.2007.01.021

来源: Elsevier

【 摘 要 】

This paper presents and studies Fredholm integral equations associated with the linear Riemann-Hilbert problems on multiply connected regions with smooth boundary curves. The kernel of these integral equations is the generalized Neumann kernel. The approach is similar to that for simply connected regions (see [R. Wegmann, A.H.M. Murid, M.M.S. Nasser. The Riemann-Hilbert problem and the generalized Neumann kernel, J. Comput. Appl. Math. 182 (2005) 388-415]). There are, however, several characteristic differences. which are mainly due to the fact. that the complement of a multiply connected region has a quite different topological structure. This implies that there is no longer perfect duality between the interior and exterior problems. We investigate the existence and uniqueness of solutions of the integral equations. In particular, we determine the exact number of linearly independent solutions of the integral equations and their adjoints. The latter determine the conditions for solvability. An analytic example on a circular annulus and several numerically calculated examples illustrate the results. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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