On the constants for some Sobolev imbeddings
| dc.creator | Morosi, C. | |
| dc.creator | Pizzocchero, L. | |
| dc.date | 2000-11-20 | |
| dc.date.accessioned | 2026-07-07T04:38:41Z | |
| dc.date.available | 2026-07-07T04:38:41Z | |
| dc.description | We consider the imbedding inequality || f ||_{L^r(R^d)} <= S_{r,n,d} || f ||_{H^{n}(R^d)}; H^{n}(R^d) is the Sobolev space (or Bessel potential space) of L^2 type and (integer or fractional) order n. We write down upper bounds for the constants S_{r, n, d}, using an argument previously applied in the literature in particular cases. We prove that the upper bounds computed in this way are in fact the sharp constants if (r=2 or) n > d/2, r=infinity, and exhibit the maximising functions. Furthermore, using convenient trial functions, we derive lower bounds on S_{r,n,d} for n > d/2, 2 < r < infinity; in many cases these are close to the previous upper bounds, as illustrated by a number of examples, thus characterizing the sharp constants with little uncertainty. | |
| dc.description | 12 pages, to appear in the Journal of Inequalities and Applications | |
| dc.identifier | https://arxiv.org/abs/math/0011141 | |
| dc.identifier | http://arxiv.org/abs/math/0011141 | |
| dc.identifier | Journal of Inequalities and Applications 6, 665-679 (2001) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60380 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.title | On the constants for some Sobolev imbeddings | |
| dc.type | text |