# A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems

created by giacomini on 27 Oct 2005
modified on 25 Sep 2008

[BibTeX]

Published Paper

Inserted: 27 oct 2005
Last Updated: 25 sep 2008

Journal: J. Differential Equations
Volume: 237
Pages: 27-60
Year: 2007

Abstract:

We prove that if $A$ is a bounded open set in $\R^2$ and the complement of $A$ satisfies suitable structural assumptions (for example it has a countable number of connected components), then $W^{1,2}(A)$ is dense in $W^{1,p}(A)$ for every $1<= p<2$. The main application of this density result is the study of stability under boundary variations for two dimensional nonlinear Neumann problems.