Startseite Mathematik Determination of lower order perturbations of a polyharmonic operator in two dimensions
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Determination of lower order perturbations of a polyharmonic operator in two dimensions

  • Rajat Bansal ORCID logo , Venkateswaran P. Krishnan ORCID logo und Rahul Raju Pattar ORCID logo EMAIL logo
Veröffentlicht/Copyright: 15. November 2024

Abstract

We study an inverse boundary value problem for a polyharmonic operator in two dimensions. We show that the Cauchy data uniquely determine all the anisotropic perturbations of orders at most m - 1 and several perturbations of orders m to 2 m - 2 under some restriction. The uniqueness proof relies on the ¯ -techniques and the method of stationary phase.

MSC 2020: 35R30; 35J40

Award Identifier / Grant number: EP/R014604/1

Funding statement: Venkateswaran P. Krishnan would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, for support and hospitality during Rich and Nonlinear Tomography – a multidisciplinary approach in 2023 where part of this work was done (supported by EPSRC Grant Number EP/R014604/1).

Acknowledgements

The authors thank Manas Kar for suggesting this problem and Masaru Ikehata for drawing our attention to the references [14, 15, 16].

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Received: 2023-10-10
Revised: 2024-07-15
Accepted: 2024-10-28
Published Online: 2024-11-15
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 10.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jiip-2023-0067/pdf
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