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We prove decay estimates in the interior for solutions to elliptic equationsin divergence form with Lipschitz continuous coefficients. The estimatesexplicitly depend on the distance from the boundary and on suitable notions offrequency of the Dirichlet boundary datum. We show that, as the frequency atthe boundary grows, the square of a suitable norm of the solution in a compactsubset of the domain decays in an inversely proportional manner with respect tothe corresponding frequency.  Under Lipschitz regularity assumptions, these estimates are essentiallyoptimal and they have important consequences for the choice of optimalmeasurements for corresponding inverse boundary value problem.

Interior decay of solutions to elliptic equations with respect to frequencies at the boundary