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arXiv · 1910.13489

Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies

Boya Liu
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Abstract

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose inaccessible portion of the boundary is contained in a hyperplane, and we are given the Cauchy data set on the complement. The uniqueness and logarithmic stability for this problem were established in [37] and [7], respectively. We establish stability estimates in the high frequency regime, with an explicit dependence on the frequency parameter, under mild regularity assumptions on the potentials, sharpening those of [7].

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Boya Liu. 2019-10-29. Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies. https://doi.org/10.3934/ipi.2020036

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