Estimates of the best Sobolev constant of the embedding of $BV(Ω)$ into $L^1(\partialΩ)$ and related shape optimization problems
| dc.creator | Saintier, Nicolas | |
| dc.date | 2007-06-07 | |
| dc.date.accessioned | 2026-07-07T08:04:31Z | |
| dc.date.available | 2026-07-07T08:04:31Z | |
| dc.description | In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality $λ_1(Ω)\|u\|_{L^1(\partialΩ)} \le \|u\|_{W^{1,1}(Ω)}$ that are independent of $Ω$. This estimates generalize those of \cite{BS} concerning the $p$-Laplacian to the case $p=1$. We apply our results to prove existence of an extremal for this embedding. We then study an optimal design problem related to $λ_1$, and eventually compute the shape derivative of the functional $Ω\toλ_1(Ω)$. As a consequence, we obtain that a ball of $\R^n$ of radius $n$ is critical for volume-preserving deformations. | |
| dc.identifier | https://arxiv.org/abs/0706.1048 | |
| dc.identifier | http://arxiv.org/abs/0706.1048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129992 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P15, 49Q10, 49Q20 | |
| dc.title | Estimates of the best Sobolev constant of the embedding of $BV(Ω)$ into $L^1(\partialΩ)$ and related shape optimization problems | |
| dc.type | text |