On domain decomposition for elliptic systems

We consider a region unbounded in at least one direction on which is defined an abstract elliptic system subject to non-homogeneous Neumann data on part (Formula presented.) of the surface that is otherwise free. We show that a quadratic form, analogous to the Dirichlet integral, becomes increasingly small on sub-regions increasingly remote from (Formula presented.). The technique is illustrated by various specific linear and nonlinear examples, including the p-Laplacian, for some of which the method must be slightly modified.