An inverse problem for Schrödinger equations with discontinuous main coefficient

Details An inverse problem for Schrödinger equations with discontinuous main coefficient An inverse problem for Schrödinger equations with discontinuous main coefficient

2008-04-10

arxiv.org/abs/0804.1714v1

Applicable Analysis (2008) 100

Mathematics

Analysis of PDEs

Scientific paper

This paper concerns the inverse problem of retrieving a stationary potential for the Schr\"odinger evolution equation in a bounded domain of RN with Dirichlet data and discontinuous principal coefficient a(x) from a single time-dependent Neumann boundary measurement. We consider that the discontinuity of a is located on a simple closed hyper-surface called the interface, and a is constant in each one of the interior and exterior domains with respect to this interface. We prove uniqueness and lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the interior domain and on the sign of the jump of a at the interface. The proof is based on a global Carleman inequality for the Schr\"odinger equation with discontinuous coefficients, result also interesting by itself.

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