Double Logarithmic Stability in the Identification of a Scalar Potential by a Partial Elliptic Dirichlet-to-Neumann Map

We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schrodinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data is imposed on the shadowed face of the boundary of the domain and the Neumann data is measured on its illuminated face. We establish a log log stability estimate for the L^2-norm (resp. the H^{-1}-norm) of H^t, for t>0, and bounded (resp. L^2) potentials.

Keywords

inverse problem; stability; Schrodinger equation.

References

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