We prove that if $A$ is bounded open subset in the plane and its complement 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 exponent p between 1 and 2. The main application of this density result is the study of stability under boundary variations for nonlinear elliptic problems under Neumann conditions.
A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems
GIACOMINI, Alessandro;TREBESCHI, Paola
2007-01-01
Abstract
We prove that if $A$ is bounded open subset in the plane and its complement 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 exponent p between 1 and 2. The main application of this density result is the study of stability under boundary variations for nonlinear elliptic problems under Neumann conditions.File in questo prodotto:
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