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
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.