Optimal logarithmic estimates in the Hardy-Sobolev space of the disk and stability results

We prove a logarithmic estimate in the Hardy-Sobolev space Hk,2, k a positive integer, of the unit disk D. This estimate extends those previously established by L. Baratchart and M. Zerner in H1,2 and by S. Chaabane and I. Feki in Hk,∞. We use it to derive logarithmic stability results for the inverse problem of identifying Robin's coefficients in corrosion detection by electrostatic boundary measurements and for a recovery interpolation scheme in the Hardy-Sobolev space Hk,2 with interpolation points located on the boundary T of the unit disk.