On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane

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: P. A. Krutitskii, A. Sasamoto
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/579457
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spelling doaj-10c4e1384b1e48feb27d810a60f936922020-11-24T21:37:08ZengHindawi LimitedInternational 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
collection DOAJ
language English
format Article
sources DOAJ
author P. A. Krutitskii
A. Sasamoto
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
author_facet P. A. Krutitskii
A. Sasamoto
author_sort P. A. Krutitskii
title 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_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_sort on the modified jump problem for the laplace equation in the exterior of cracks in a plane
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2012-01-01
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.
url http://dx.doi.org/10.1155/2012/579457
work_keys_str_mv AT pakrutitskii onthemodifiedjumpproblemforthelaplaceequationintheexteriorofcracksinaplane
AT asasamoto onthemodifiedjumpproblemforthelaplaceequationintheexteriorofcracksinaplane
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