Astala and Päivärinta solved Calderón Inverse problem in the plane for the conductivity equation by introducing quasiconformal machinary. In this work we combine properties of Cauchy transform with careful analysis of the non elliptic Schrodingers to show how the recent uniqueness result of Buckgheim for the Schrondinger potentials yields a reconstruction procedure for potentials with half derivatives square integrable. Moreover the result is sharp. This is a joint work with K.Astala and K.M Rogers.
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