  Brady, Creighton and Thorne have argued that, in numerical relativity
simulations of the inspiral of binary black holes, if one uses lapse and shift
functions satisfying the ``minimal strain equations'' (MSE), then the
coordinates might be kept co-rotating, the metric components would then evolve
on the very slow inspiral timescale, and the computational demands would thus
be far smaller than for more conventional slicing choices. In this paper, we
derive simple, testable criteria for the MSE to be strongly elliptic, thereby
guaranteeing the existence and uniqueness of the solution to the Dirichlet
boundary value problem. We show that these criteria are satisfied in a test-bed
metric for inspiraling binaries, and we argue that they should be satisfied
quite generally for inspiraling binaries. If the local existence and uniqueness
that we have proved holds globally, then, for appropriate boundary values, the
solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and
keeps the metric evolving slowly) will be the unique solution and thus should
be reproduced by (sufficiently accurate and stable) numerical integrations.
