Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 77, pp. 110.
A property of Sobolev spaces on complete Riemannian manifolds
Ognjen Milatovic
Abstract:
Let
be a complete Riemannian manifold with metric
and the Riemannian volume form
.
We consider the
valued
functions
and
on
,
where
is a Sobolev space on
and
is its dual. We give a sufficient condition for the equality of
and the integral of
over
,
where
is the duality between
and
.
This is an extension to
complete Riemannian manifolds of a result of H. Brezis and
F. E. Browder.
Submitted June 25, 2005. Published July 8, 2005.
Math Subject Classifications: 58J05.
Key Words: Complete Riemannian manifold; Sobolev space
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Ognjen Milatovic
Department of Mathematics and Statistics
University of North Florida
Jacksonville, FL 32224, USA
email: omilatov@unf.edu 
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