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.

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