International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 279-282

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

M. I. Hassan

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 9028, Jeddah, Saudi Arabia

Received 19 April 1983

Copyright © 1984 M. I. Hassan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.