Remarks on the Extremal Functions for the Moser-Trudinger Inequalities
| dc.creator | Li, Yuxiang | |
| dc.date | 2005-04-15 | |
| dc.date | 2005-07-28 | |
| dc.date.accessioned | 2026-07-07T05:19:08Z | |
| dc.date.available | 2026-07-07T05:19:08Z | |
| dc.description | We will show in this paper that if $λ$ is very close to 1, then $$I(M,λ,m)= \sup_{u\in H^{1,n}_0(M) ,\int_M|\nabla u|^ndV=1}\int_Ω(e^{α_n |u|^\frac{n}{n-1}}-λ\sum\limits_{k=1}^m\frac{|α_nu^\frac{n}{n-1}|^k} {k!})dV,$$ can be attained, where $M$ is a compact manifold with boundary. This result gives a counter example to the conjecture of de Figueiredo, do ó, and Ruf in their paper titled "On a inequality by N.Trudinger and J.Moser and related elliptic equations" (Comm. Pure. Appl. Math.,{\bf 55}:135-152, 2002). | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504317 | |
| dc.identifier | http://arxiv.org/abs/math/0504317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74911 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J05 | |
| dc.title | Remarks on the Extremal Functions for the Moser-Trudinger Inequalities | |
| dc.type | text |