The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces
We study the Dirichlet problem for the equation Δu−k2u=0 in the exterior of nonclosed Lipschitz surfaces in R3. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral represen...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/302628 |
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| author | P. A. Krutitskii |
| author_facet | P. A. Krutitskii |
| author_sort | P. A. Krutitskii |
| collection | DOAJ |
| description | We study the Dirichlet problem for the equation Δu−k2u=0 in the exterior of nonclosed Lipschitz surfaces in R3. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and
uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable. |
| format | Article |
| id | doaj-art-dd7026d9bf6344c6aa2b3a58a039ff01 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dd7026d9bf6344c6aa2b3a58a039ff012025-02-03T06:07:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/302628302628The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz SurfacesP. A. Krutitskii0KIAM, Miusskaya Sq. 4, Moscow 125047, RussiaWe study the Dirichlet problem for the equation Δu−k2u=0 in the exterior of nonclosed Lipschitz surfaces in R3. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.http://dx.doi.org/10.1155/2013/302628 |
| spellingShingle | P. A. Krutitskii The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces International Journal of Mathematics and Mathematical Sciences |
| title | The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces |
| title_full | The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces |
| title_fullStr | The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces |
| title_full_unstemmed | The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces |
| title_short | The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces |
| title_sort | dirichlet problem for the equation δu k2u 0 in the exterior of nonclosed lipschitz surfaces |
| url | http://dx.doi.org/10.1155/2013/302628 |
| work_keys_str_mv | AT pakrutitskii thedirichletproblemfortheequationduk2u0intheexteriorofnonclosedlipschitzsurfaces AT pakrutitskii dirichletproblemfortheequationduk2u0intheexteriorofnonclosedlipschitzsurfaces |