The $L^p$ Dirichlet Problem for Elliptic Systems on Lipschitz Domains
| dc.creator | Shen, Zhongwei | |
| dc.date | 2004-11-05 | |
| dc.date.accessioned | 2026-07-07T05:14:00Z | |
| dc.date.available | 2026-07-07T05:14:00Z | |
| dc.description | We develop a new approach to the $L^p$ Dirichlet problem via $L^2$ estimates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyharmonic equation on a bounded Lipschitz domain $Ω$ in $R^n$. For $n\ge 4$ and $2-ε<p<2(n-1)/(n-3)+ε$, we establish the solvability of the Dirichlet problem with boundary value data in $L^p(\partialΩ)$. In the case of the polyharmonic equation $Δ^{\ell}u=0$ with $\ell\ge 2$, the range of $p$ is sharp if $4\le n \le 2\ell +1$. | |
| dc.identifier | https://arxiv.org/abs/math/0411120 | |
| dc.identifier | http://arxiv.org/abs/math/0411120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73119 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 35J55:35J40 | |
| dc.title | The $L^p$ Dirichlet Problem for Elliptic Systems on Lipschitz Domains | |
| dc.type | text |