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

Boya Liu

doi:10.3934/ipi.2020036

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2020, Volume 14, Issue 5: 783-796. Doi: 10.3934/ipi.2020036

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

Boya Liu^,

Department of Mathmatics, University of California, Irvine, Irvine, CA 92697, USA

^*Corresponding author: Boya Liu
^*Corresponding author: Boya Liu

Received: October 31, 2019

Revised: March 31, 2020

Published: July 2020

The research is partially supported by the National Science Foundation (DMS 1815922)

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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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Mathematics Subject Classification: Primary: 35R30, 35J40.

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