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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000284 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |