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In this paper we study the inverse boundary value problem of determining thepotential in the Schr\"{o}dinger equation from the knowledge of theDirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem inthe sense that, under general settings, the optimal stability estimate is oflogarithmic type. In this work, a Lipschitz type stability is establishedassuming a priori that the potential is piecewise constant with a bounded knownnumber of unknown values.

Lipschitz stability of an inverse boundary value problem for a Schr\"{o}dinger type equation