Inverse boundary value problems for the perturbed polyharmonic operator
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- by Katsiaryna Krupchyk, Matti Lassas and Gunther Uhlmann PDF
- Trans. Amer. Math. Soc. 366 (2014), 95-112 Request permission
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 $m=1$.References
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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
- MR Author ID: 175790
- Email: gunther@math.washington.edu
- Received by editor(s): March 13, 2011
- Received by editor(s) in revised form: September 27, 2011
- Published electronically: July 3, 2013
- © Copyright 2013 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 366 (2014), 95-112
- MSC (2010): Primary 35R30, 31B20, 31B30, 35J40
- DOI: https://doi.org/10.1090/S0002-9947-2013-05713-3
- MathSciNet review: 3118392