首页|STABILITY FOR AN INVERSE SOURCE PROBLEM OF THE BIHARMONIC OPERATOR
STABILITY FOR AN INVERSE SOURCE PROBLEM OF THE BIHARMONIC OPERATOR
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NSTL
Siam Publications
In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in R3. An eigenvalue problem is considered for the bi-Schro"\dinger operator \Delta 2 + V (x) on a ball which contains the support of the potential V. A Weyl-type law is proved for the upper bounds of spherical normal derivatives of both the eigenfunctions \phi and their Laplacian \Delta \phi corresponding to the bi-Schro"\dinger operator. These types of upper bounds was proved by Hassell and Tao [Math. Res. Lett., 9 (2012), pp. 289305] for the Schro"\dinger operator. The meromorphic continuation is investigated for the resolvent of the bi-Schro"\dinger operator, which is shown to have a resonance-free region and an estimate of L2comp - L2lo c type for the resolvent. As an application, we prove a bound of the analytic continuation of the data with respect to the frequency. Finally, the stability estimate is derived for the inverse source problem. The estimate consists of the Lipschitz-type data discrepancy and the high-frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases.
NSTL
Siam Publications
