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 , 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 , 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.