Calculus of Variations and Geometric Measure Theory

A. Giacomini - P. Trebeschi

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


Published Paper

Inserted: 27 oct 2005
Last Updated: 25 sep 2008

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


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.