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
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