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

M. I. Hassan

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-4

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.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:912842

DOI: 10.1155/S0161171284000284

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