A note on extremal functions for sharp Sobolev inequalities
| dc.contributor.author | Barbosa, Ezequiel | |
| dc.contributor.author | Montenegro, Marcos | |
| dc.date.accessioned | 2021-08-11T20:35:55Z | |
| dc.date.available | 2021-08-11T20:35:55Z | |
| dc.date.issued | 2007-06-15 | |
| dc.description.abstract | In this note we prove that any compact Riemannian manifold of dimension n ≥ 4 which is non-conformal to the standard n-sphere and has positive Yamabe invariant admits infinitely many conformal metrics with nonconstant positive scalar curvature on which the classical sharp Sobolev inequalities admit extremal functions. In particular we show the existence of compact Riemannian manifolds with nonconstant positive scalar curvature for which extremal functions exist. Our proof is simple and bases on results of the best constants theory and Yamabe problem. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 5 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Barbosa, E., & Montenegro, M. (2007). A note on extremal functions for sharp Sobolev inequalities. <i>Electronic Journal of Differential Equations, 2007</i>(87), pp. 1-5. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14282 | |
| 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, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Extremal functions | |
| dc.subject | Optimal Sobolev inequalities | |
| dc.subject | Conformal deformations | |
| dc.title | A note on extremal functions for sharp Sobolev inequalities | |
| dc.type | Article |