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We consider Calderón's inverse problem on planar domains Ω with conductivities in fractional Sobolev spaces. When Ω is Lipschitz, the problem was shown to be stable in the  L  2 -sense in Clop  et al.  [Stability of calderón's inverse conductivity problem in the plane for discontinuous conductivities,  Inverse Probl. Imaging  4  (2010), 49–91]. We remove the Lipschitz condition on the boundary. To this end, we analyse the Sobolev regularity of the characteristic function of Ω. For Ω a quasiball, we compute ||χ Ω ||  W   s , p  (ℝ  d  )  in terms of the δ-neighbourhoods of the boundary.

THE SOBOLEV NORM OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS TO THE CALDERÓN INVERSE PROBLEM