Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

Brown R.M.; Gauthier L.D.

doi:10.3934/ipi.2022006

Article Contents

2022, Volume 16, Issue 4: 943-966. Doi: 10.3934/ipi.2022006

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Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

Brown R.M. and
Gauthier L.D.^,

Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA

^*Corresponding author: L.D. Gauthier
^*Corresponding author: L.D. Gauthier

Received: July 31, 2021

Revised: November 30, 2021

Early access: February 2022

Published: August 2022

R.M. Brown is partially supported by a grant from the Simons Foundation (#422756)

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Abstract

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J40.

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