Abstract and Applied Analysis
Volume 2005 (2005), Issue 7, Pages 691-705

Weak formulation of singular differential expressions in spaces of functions with minimal derivatives

M. A. El-Gebeily

Mathematical Sciences Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 4 October 2004

Copyright © 2005 M. A. El-Gebeily. 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.


A weak formulation for singular symmetric differential expressions is presented in spaces of functions which possess minimal differentiability requirements. These spaces are used to characterize the domains of the various operators associated with such expressions. In particular, domains of self-adjoint differential operators are characterized.