The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks
This paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition ∂u/∂n+hu=f is given on the boundary of the domain. The skip of the function u+−u−=g and the modified skip of the normal derivatives (∂u/∂n)+−(∂u/∂n)−+hu+=f are given on...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/91983 |
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| _version_ | 1832565004554993664 |
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| author | Dagmar Medková |
| author_facet | Dagmar Medková |
| author_sort | Dagmar Medková |
| collection | DOAJ |
| description | This paper studies the third problem for the Laplace equation on a
bounded planar domain with inside cracks. The third condition
∂u/∂n+hu=f
is given on the boundary of the
domain. The skip of the function u+−u−=g
and the modified
skip of the normal derivatives (∂u/∂n)+−(∂u/∂n)−+hu+=f
are given on cracks. The
solution is looked for in the form of the sum of a modified
single-layer potential and a double-layer potential. The solution
of the corresponding integral equation is constructed. |
| format | Article |
| id | doaj-art-06c63c890656497584ed4ede23ed2f45 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-06c63c890656497584ed4ede23ed2f452025-02-03T01:09:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/9198391983The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracksDagmar Medková0Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Karlovo Nám. 13, 12135 Praha 2, Czech RepublicThis paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition ∂u/∂n+hu=f is given on the boundary of the domain. The skip of the function u+−u−=g and the modified skip of the normal derivatives (∂u/∂n)+−(∂u/∂n)−+hu+=f are given on cracks. The solution is looked for in the form of the sum of a modified single-layer potential and a double-layer potential. The solution of the corresponding integral equation is constructed.http://dx.doi.org/10.1155/IJMMS/2006/91983 |
| spellingShingle | Dagmar Medková The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks International Journal of Mathematics and Mathematical Sciences |
| title | The solution of the third problem for the Laplace equation on
planar domains with smooth boundary and inside cracks and modified
jump conditions on cracks |
| title_full | The solution of the third problem for the Laplace equation on
planar domains with smooth boundary and inside cracks and modified
jump conditions on cracks |
| title_fullStr | The solution of the third problem for the Laplace equation on
planar domains with smooth boundary and inside cracks and modified
jump conditions on cracks |
| title_full_unstemmed | The solution of the third problem for the Laplace equation on
planar domains with smooth boundary and inside cracks and modified
jump conditions on cracks |
| title_short | The solution of the third problem for the Laplace equation on
planar domains with smooth boundary and inside cracks and modified
jump conditions on cracks |
| title_sort | solution of the third problem for the laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks |
| url | http://dx.doi.org/10.1155/IJMMS/2006/91983 |
| work_keys_str_mv | AT dagmarmedkova thesolutionofthethirdproblemforthelaplaceequationonplanardomainswithsmoothboundaryandinsidecracksandmodifiedjumpconditionsoncracks AT dagmarmedkova solutionofthethirdproblemforthelaplaceequationonplanardomainswithsmoothboundaryandinsidecracksandmodifiedjumpconditionsoncracks |