Tadeusz Iwaniec and Jani Onninen
Abstract: Let X and Y be bounded multiply connected Lipschitz domains in $\mathbb R^2$. We consider the class $H_p (X, Y)$ of homeomorphisms $h : X\to Y$ in the Sobolev space $W^{1,p} (X, \mathbb R^2)$. We prove that the weak and strong closures of $H_p (X, Y)$, $2 \le p< \infty$, are equal. The importance of this result to the existence theory in the calculus of variations and anticipated applications to nonlinear elasticity are captured by Theorem 1.5.
ArXiv: 1201.3864