Determining rough first order perturbations of the polyharmonic operator

Yernat Assylbekov; Karthik Iyer

doi:10.3934/ipi.2019047

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2019, Volume 13, Issue 5: 1045-1066. Doi: 10.3934/ipi.2019047

This issue Previous Article Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data Next Article A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media

Determining rough first order perturbations of the polyharmonic operator

Yernat Assylbekov^1, and
Karthik Iyer^2,

1.
Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
2.
The Vanguard Group, Malvern, PA 19335, USA

Received: November 2018

Published: July 2019

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Abstract

We show that the knowledge of Dirichlet to Neumann map for rough $ A $ and $ q $ in $ (-\Delta)^m +A\cdot D +q $ for $ m \geq 2 $ for a bounded domain in $ \mathbb{R}^n $, $ n \geq 3 $ determines $ A $ and $ q $ uniquely. This unique identifiability is proved via construction of complex geometrical optics solutions with sufficient decay of remainder terms, by using property of products of functions in Sobolev spaces.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J62.

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