Determination of lower order perturbations of the polyharmonic operator from partial boundary data

Abstract

We consider a perturbed polyharmonic operator of order defined on a bounded simply connected domain with smooth connected boundary of the form:

where and stands for the greatest integer function. In the biharmonic case, such operators arise in the study of certain elasticity and buckling problems. We study an inverse problem involving and show that all the coefficients , and can be recovered from partial Dirichlet-to-Neumann (D-N) data on the boundary.

Keywords:

• Calderón-type inverse problem
• perturbed polyharmonic operator
• Carleman estimates

AMS Subject Classifications:

• 35G15
• 35J40
• 35R30
• 45Q05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the second named author was supported by NSF [grant number DMS 1109417] and German DAAD Research Stays grant. The work of both the authors was supported by Airbus Group Corporate Foundation Chair “Mathematics of Complex Systems” established at TIFR Centre for Applicable Mathematics and TIFR International Centre for Theoretical Sciences.