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Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation

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  • M. I. Hassan

Abstract

The present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet's problem for a linear second-order elliptic equation L u = 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 W 1 . By means of an example it is shown that the obtained result is exact.

Suggested Citation

  • M. I. Hassan, 1984. "Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 7, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:912842
    DOI: 10.1155/S0161171284000284
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