A remark on precomposition on H1/2(S1) and ε-identifiability of disks in tomography

We consider the inverse conductivity problem with one measurement for the equationdiv((σ1+(σ2−σ1)χω)∇u)=0 determining the unknown inclusion ω included in Ω. We suppose that Ω is the unit disk of R2. With the tools of the conformal mappings, of elementary Fourier analysis and by studying how W1,∞(S1,S1) diffeomorphisms act by precomposition on the Sobolev space H1/2(S1), we show how to approximate the Dirichlet-to-Neumann map when the original inclusion ω is a ε-approximation of a disk. This enables us to give some uniqueness and stability results.