A property of Sobolev spaces on complete Riemannian manifolds
| dc.contributor.author | Milatovic, Ognjen | |
| dc.date.accessioned | 2021-05-28T19:09:14Z | |
| dc.date.available | 2021-05-28T19:09:14Z | |
| dc.date.issued | 2005-07-08 | |
| dc.description.abstract | Let (M, g) be a complete Riemannian manifold with metric g and the Riemannian volume form dv. We consider the ℝk-valued functions T ∈ [W-1,2(M) ∩ L1loc (M)]k and u ∈ [W1,2(M)]k on M, where [W1,2(M)]k is a Sobolev space on M and [W-1,2(M)]k is its dual. We give a sufficient condition for the equality of ⟨T, u⟩ and the integral of (T ∙ u) over M, where ⟨∙, ∙⟩ is the duality between [W-1,2(M)]k. This is an extension to complete Riemannian manifolds of a result of H. Brézis and F. E. Browder. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Milatovic, O. (2005). A property of Sobolev spaces on complete Riemannian manifolds. <i>Electronic Journal of Differential Equations, 2005</i>(77), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13678 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Complete Riemannian manifold | |
| dc.subject | Sobolev space | |
| dc.title | A property of Sobolev spaces on complete Riemannian manifolds | |
| dc.type | Article |