An integral equation related to the exterior riemann-hilbert problem on region with corners
Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 20...
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| Format: | Article |
| Language: | English |
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Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia
2008
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| Online Access: | http://eprints.utm.my/7102/ http://eprints.utm.my/7102/1/MuniraIsmail2008_AnIntegralEquationRelated.pdf |
| _version_ | 1848891404316573696 |
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| author | Zamzamir, Zamzana Ismail, Munira Mohamed Murid, Ali Hassan |
| author_facet | Zamzamir, Zamzana Ismail, Munira Mohamed Murid, Ali Hassan |
| author_sort | Zamzamir, Zamzana |
| building | UTeM Institutional Repository |
| collection | Online Access |
| description | Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 2007 provides a numerical solution of the interior RH problem on region with corners via Nasser’s method together with Swarztrauber’s approach, but Ismail does not develop any integral equation related to exterior RH problem on region with corners. In this paper, we introduce a new integral equation related to the exterior RH problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. We obtain a new integral equation that adopts Ismail’s method which does not involve conformal mapping. This result is a generalization of the integral equation developed by Nasser for the exterior RH problem on smooth region. The solvability of the integral equation in accordance with the Fredholm alternative theorem is presented. The proof of the equivalence of our integral equation to the RH problem is also provided
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| first_indexed | 2025-11-15T20:57:26Z |
| format | Article |
| id | utm-7102 |
| institution | Universiti Teknologi Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:57:26Z |
| publishDate | 2008 |
| publisher | Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | utm-71022017-10-22T07:56:22Z http://eprints.utm.my/7102/ An integral equation related to the exterior riemann-hilbert problem on region with corners Zamzamir, Zamzana Ismail, Munira Mohamed Murid, Ali Hassan QA Mathematics Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 2007 provides a numerical solution of the interior RH problem on region with corners via Nasser’s method together with Swarztrauber’s approach, but Ismail does not develop any integral equation related to exterior RH problem on region with corners. In this paper, we introduce a new integral equation related to the exterior RH problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. We obtain a new integral equation that adopts Ismail’s method which does not involve conformal mapping. This result is a generalization of the integral equation developed by Nasser for the exterior RH problem on smooth region. The solvability of the integral equation in accordance with the Fredholm alternative theorem is presented. The proof of the equivalence of our integral equation to the RH problem is also provided Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2008 Article PeerReviewed application/pdf en http://eprints.utm.my/7102/1/MuniraIsmail2008_AnIntegralEquationRelated.pdf Zamzamir, Zamzana and Ismail, Munira and Mohamed Murid, Ali Hassan (2008) An integral equation related to the exterior riemann-hilbert problem on region with corners. Journal of Fundamental Sciences, 4 (2). pp. 369-377. ISSN 1823-626X http://jfs.ibnusina.utm.my/index.php/jfs/issue/view/22/showToc |
| spellingShingle | QA Mathematics Zamzamir, Zamzana Ismail, Munira Mohamed Murid, Ali Hassan An integral equation related to the exterior riemann-hilbert problem on region with corners |
| title | An integral equation related to the exterior riemann-hilbert problem on region with corners |
| title_full | An integral equation related to the exterior riemann-hilbert problem on region with corners |
| title_fullStr | An integral equation related to the exterior riemann-hilbert problem on region with corners |
| title_full_unstemmed | An integral equation related to the exterior riemann-hilbert problem on region with corners |
| title_short | An integral equation related to the exterior riemann-hilbert problem on region with corners |
| title_sort | integral equation related to the exterior riemann-hilbert problem on region with corners |
| topic | QA Mathematics |
| url | http://eprints.utm.my/7102/ http://eprints.utm.my/7102/ http://eprints.utm.my/7102/1/MuniraIsmail2008_AnIntegralEquationRelated.pdf |