Biharmonic Green functions
The harmonic Green and Neumann function and a particular Robin function are used to construct bi-harmonic Green, Neumann and particular Robin functions. Moreover hybrid bi-harmonic Green functions are given. They all are constructed via a convolution of the mentioned harmonic particular fundamental...
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2006-11-01
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| Series: | Le Matematiche |
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| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/130 |
| _version_ | 1818359075826565120 |
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| author | Heinrich Begehr |
| author_facet | Heinrich Begehr |
| author_sort | Heinrich Begehr |
| collection | DOAJ |
| description | The harmonic Green and Neumann function and a particular Robin function are used to construct bi-harmonic Green, Neumann and particular Robin functions. Moreover hybrid bi-harmonic Green functions are given. They all are constructed via a convolution of the mentioned harmonic particular fundamental solutions. In case of the unit disc they are explicitly expressed. <br />Besides these 9 bi-harmonic Green functions there is another bi-harmonic Green function in explicit form for the unit disc not defined by convolution. Related boundary value problems are not all well posed. In case they are, the unique solutions are given. For the other cases solvability conditions are determined and the unique solutions found. There are all together 12 Dirichlet kind boundary value problems for the inhomogeneous bi-harmonic equation treated. The investigation is restricted to the two dimensional case and complex notation is used.<br /> |
| first_indexed | 2024-12-13T20:39:08Z |
| format | Article |
| id | doaj.art-5d747f19885d449aad96e2cbe8a4581b |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-12-13T20:39:08Z |
| publishDate | 2006-11-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-5d747f19885d449aad96e2cbe8a4581b2022-12-21T23:32:12ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982006-11-01612395405111Biharmonic Green functionsHeinrich BegehrThe harmonic Green and Neumann function and a particular Robin function are used to construct bi-harmonic Green, Neumann and particular Robin functions. Moreover hybrid bi-harmonic Green functions are given. They all are constructed via a convolution of the mentioned harmonic particular fundamental solutions. In case of the unit disc they are explicitly expressed. <br />Besides these 9 bi-harmonic Green functions there is another bi-harmonic Green function in explicit form for the unit disc not defined by convolution. Related boundary value problems are not all well posed. In case they are, the unique solutions are given. For the other cases solvability conditions are determined and the unique solutions found. There are all together 12 Dirichlet kind boundary value problems for the inhomogeneous bi-harmonic equation treated. The investigation is restricted to the two dimensional case and complex notation is used.<br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/130biharmonic GreenNeumannRobinhybrid Green functionsboundary value problemsinhomogeneous biharmonic equationunit disc in complex plane |
| spellingShingle | Heinrich Begehr Biharmonic Green functions Le Matematiche biharmonic Green Neumann Robin hybrid Green functions boundary value problems inhomogeneous biharmonic equation unit disc in complex plane |
| title | Biharmonic Green functions |
| title_full | Biharmonic Green functions |
| title_fullStr | Biharmonic Green functions |
| title_full_unstemmed | Biharmonic Green functions |
| title_short | Biharmonic Green functions |
| title_sort | biharmonic green functions |
| topic | biharmonic Green Neumann Robin hybrid Green functions boundary value problems inhomogeneous biharmonic equation unit disc in complex plane |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/130 |
| work_keys_str_mv | AT heinrichbegehr biharmonicgreenfunctions |