On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane
The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under cert...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/579457 |
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| author | P. A. Krutitskii A. Sasamoto |
| author_facet | P. A. Krutitskii A. Sasamoto |
| author_sort | P. A. Krutitskii |
| collection | DOAJ |
| description | The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The integral representation and integral equation are essentially simpler than those derived for this problem earlier. The singularities at the ends of the cracks are investigated. |
| format | Article |
| id | doaj-art-10c4e1384b1e48feb27d810a60f93692 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-10c4e1384b1e48feb27d810a60f936922025-02-03T01:02:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/579457579457On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a PlaneP. A. Krutitskii0A. Sasamoto1KIAM, Miusskaya Sq. 4, Moscow 125047, RussiaAIST, 1-2-1 Namiki, Tsukuba, Ibaraki 305-8564, JapanThe boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The integral representation and integral equation are essentially simpler than those derived for this problem earlier. The singularities at the ends of the cracks are investigated.http://dx.doi.org/10.1155/2012/579457 |
| spellingShingle | P. A. Krutitskii A. Sasamoto On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane International Journal of Mathematics and Mathematical Sciences |
| title | On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane |
| title_full | On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane |
| title_fullStr | On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane |
| title_full_unstemmed | On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane |
| title_short | On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane |
| title_sort | on the modified jump problem for the laplace equation in the exterior of cracks in a plane |
| url | http://dx.doi.org/10.1155/2012/579457 |
| work_keys_str_mv | AT pakrutitskii onthemodifiedjumpproblemforthelaplaceequationintheexteriorofcracksinaplane AT asasamoto onthemodifiedjumpproblemforthelaplaceequationintheexteriorofcracksinaplane |