A property of Radon measures in Sobolev spaces and some applications
by
Xiangsheng Xu
Mississippi State University

Let \nu be a signed Radon measure on R^N. We prove that if \nu in W^{-1, p'}(R^N), the dual space of W^{1, p}(R^N), where 1 <= p < N, and p' = \fracpp-1, then (\nu, u) = \intu  d\nu whenever the the right hand side exists. Some applications are also described.

Date received: April 10, 1999