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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/302628 |
| id |
doaj-dd7026d9bf6344c6aa2b3a58a039ff01 |
|---|---|
| record_format |
Article |
| spelling |
doaj-dd7026d9bf6344c6aa2b3a58a039ff012020-11-25T01:05:34ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
P. A. Krutitskii |
| 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 |
| author_facet |
P. A. Krutitskii |
| author_sort |
P. A. Krutitskii |
| title |
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_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_sort |
dirichlet problem for the equation δu−k2u=0 in the exterior of nonclosed lipschitz surfaces |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2013-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2013/302628 |
| work_keys_str_mv |
AT pakrutitskii thedirichletproblemfortheequationduk2u0intheexteriorofnonclosedlipschitzsurfaces AT pakrutitskii dirichletproblemfortheequationduk2u0intheexteriorofnonclosedlipschitzsurfaces |
| _version_ |
1725193810333401088 |