  We prove decay estimates in the interior for solutions to elliptic equations
in divergence form with Lipschitz continuous coefficients. The estimates
explicitly depend on the distance from the boundary and on suitable notions of
frequency of the Dirichlet boundary datum. We show that, as the frequency at
the boundary grows, the square of a suitable norm of the solution in a compact
subset of the domain decays in an inversely proportional manner with respect to
the corresponding frequency.
  Under Lipschitz regularity assumptions, these estimates are essentially
optimal and they have important consequences for the choice of optimal
measurements for corresponding inverse boundary value problem.
