Determining the first order perturbation of a polyharmonic operator on admissible manifolds

2015/08/15 by Assylbekov, Yernat M., Yang, Yang · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.03706

Abstract

We consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator \mathcal L_g,X,q, with X being a W^1,∞ vector field and q being an L^∞ function on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. We show that the knowledge of the Dirichlet-to-Neumann determines X and q uniquely. The method is based on the construction of complex geometrical optics solutions using the Carleman estimate for the Laplace-Beltrami operator due to Dos Santos Ferreira, Kenig, Salo and Uhlmann. Notice that the corresponding uniqueness result does not hold for the first order perturbation of the Laplace-Beltrami operator.

Cited by

• Stability of inverse boundary value problem for the fourth-order Schrödinger equation
• Well-posedness for the biharmonic scattering problem for a penetrable obstacle

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