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arXiv · 1103.0113

Determining a first order perturbation of the biharmonic operator by partial boundary measurements

Katsiaryna Krupchyk·Matti Lassas·Gunther Uhlmann
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Abstract

We consider an operator $Δ^2 + A(x)\cdot D+q(x)$ with the Navier boundary conditions on a bounded domain in $R^n$, $n\ge 3$. We show that a first order perturbation $A(x)\cdot D+q$ can be determined uniquely by measuring the Dirichlet--to--Neumann map on possibly very small subsets of the boundary of the domain. Notice that the corresponding result does not hold in general for a first order perturbation of the Laplacian.

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Katsiaryna Krupchyk, Matti Lassas, Gunther Uhlmann. 2011-03-01. Determining a first order perturbation of the biharmonic operator by partial boundary measurements. https://arxiv.org/abs/1103.0113

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