A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems
| dc.creator | Giacomini, Alessandro | |
| dc.creator | Trebeschi, Paola | |
| dc.date | 2005-10-27 | |
| dc.date.accessioned | 2026-07-07T06:47:59Z | |
| dc.date.available | 2026-07-07T06:47:59Z | |
| dc.description | We prove that if $\Om \subseteq \R^2$ is bounded and $\R^2 \setminus \Om$ satisfies suitable structural assumptions (for example it has a countable number of connected components), then $W^{1,2}(\Om)$ is dense in $W^{1,p}(\Om)$ for every $1\le p<2$. The main application of this density result is the study of stability under boundary variations for nonlinear Neumann problems of the form $$ \begin{cases} -{\rm div} A(x,\nabla u)+B(x,u)=0 & \text{in}\Om, \\ A(x,\nabla u)\cdot ν=0 & \text{on}\partial \Om, \end{cases} $$ where $A:\R^2\times \R^2 \to \R^2$ and $B:\R^2 \times \R \to \R$ are Carathéodory functions which satisfy standard monotonicity and growth conditions of order $p$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510590 | |
| dc.identifier | http://arxiv.org/abs/math/0510590 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103836 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J65, 31A15, 47H05, 49J45 | |
| dc.title | A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems | |
| dc.type | text |