  Let X and Y be bounded multiply connected Lipschitz domains in \R^2. We
consider the class H_p (X, Y) of homeomorphisms h : X -> Y in the Sobolev space
W^{1,p} (X, \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.
