Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation
The present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet's problem for a linear second-order elliptic equation Lu=f. With the aid of special weighted Hilbert spaces of locally square integrable functions, we determine the nature of singulari...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000284 |
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| _version_ | 1832553555146309632 |
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| author | M. I. Hassan |
| author_facet | M. I. Hassan |
| author_sort | M. I. Hassan |
| collection | DOAJ |
| description | The present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet's problem for a linear second-order elliptic equation Lu=f. With the aid of special weighted Hilbert spaces of locally square integrable functions, we determine the nature of singularities that f can have near the boundary, in order that such classical solutions are in the Sobolev space W1. By means of an example it is shown that the obtained result is exact. |
| format | Article |
| id | doaj-art-80483d94b4fe4f58b4970ea709fc80f5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-80483d94b4fe4f58b4970ea709fc80f52025-02-03T05:53:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017227928210.1155/S0161171284000284Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equationM. I. Hassan0Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 9028, Jeddah, Saudi ArabiaThe present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet's problem for a linear second-order elliptic equation Lu=f. With the aid of special weighted Hilbert spaces of locally square integrable functions, we determine the nature of singularities that f can have near the boundary, in order that such classical solutions are in the Sobolev space W1. By means of an example it is shown that the obtained result is exact.http://dx.doi.org/10.1155/S0161171284000284linear second-order elliptic equationDirichlet's problemclassical solutionsSobolev spacesweighted Hilbert spaces of locally square integrable functions. |
| spellingShingle | M. I. Hassan Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation International Journal of Mathematics and Mathematical Sciences linear second-order elliptic equation Dirichlet's problem classical solutions Sobolev spaces weighted Hilbert spaces of locally square integrable functions. |
| title | Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation |
| title_full | Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation |
| title_fullStr | Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation |
| title_full_unstemmed | Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation |
| title_short | Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation |
| title_sort | integrability of derivations of classical solutions of dirichlet s problem for an elliptic equation |
| topic | linear second-order elliptic equation Dirichlet's problem classical solutions Sobolev spaces weighted Hilbert spaces of locally square integrable functions. |
| url | http://dx.doi.org/10.1155/S0161171284000284 |
| work_keys_str_mv | AT mihassan integrabilityofderivationsofclassicalsolutionsofdirichletsproblemforanellipticequation |