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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inverse boundary value problems for the perturbed polyharmonic operator


Authors: Katsiaryna Krupchyk, Matti Lassas and Gunther Uhlmann
Journal: Trans. Amer. Math. Soc. 366 (2014), 95-112
MSC (2010): Primary 35R30, 31B20, 31B30, 35J40
Published electronically: July 3, 2013
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Abstract: We show that a first order perturbation $ A(x)\cdot D+q(x)$ of the polyharmonic operator $ (-\Delta )^m$, $ m\ge 2$, can be determined uniquely from the set of the Cauchy data for the perturbed polyharmonic operator on a bounded domain in $ \mathbb{R}^n$, $ n\ge 3$. Notice that the corresponding result does not hold in general when $ m=1$.


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Additional Information

Katsiaryna Krupchyk
Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, Finland
Email: katya.krupchyk@helsinki.fi

Matti Lassas
Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, Finland
Email: matti.lassas@helsinki.fi

Gunther Uhlmann
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Email: gunther@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05713-3
PII: S 0002-9947(2013)05713-3
Received by editor(s): March 13, 2011
Received by editor(s) in revised form: September 27, 2011
Published electronically: July 3, 2013
Article copyright: © Copyright 2013 American Mathematical Society