Growth estimates in the Hardy-Sobolev space of an annular domain with applications

We give an explicit estimate on the growth of functions in the Hardy-Sobolev space H-k,H-2(G(s)) of an annulus. We apply this result, first, to find an upper bound on the rate of convergence of a recovery interpolation scheme in H-1,H-2(G(s)) with points located on the outer boundary of G(s). We also apply this result for the study of a geometric inverse problem, namely we derive an explicit upper bound on the area of an unknown cavity in a bounded planar domain from the difference of two electrostatic potentials measured on the boundary, when the cavity is present and when it is not. (C) 2009 Elsevier Inc. All rights reserved.