Abstract and Applied Analysis 
Volume 2005 (2005), Issue 7, Pages 691-705
doi:10.1155/AAA.2005.691

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

Abstract

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.