Inverse problems for the perturbed polyharmonic operator with coefficients in Sobolev spaces with non-positive order. (1st September 2016)

• Record Type: Journal Article
• Authors: Assylbekov, Yernat M
• Is Part Of: Inverse problems. Volume 32:Number 10(2016:Oct.)
• Publication Date: 2016-09-01
• Subjects: inverse problems -- polyharmonic operators -- Dirichlet-to-Neumann map; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/10/105009
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in R n, n ≥ 3, for the perturbed polyharmonic operator ( − Δ ) m + A · D + q, m ≥ 2, with 2 n > m, A ∊ W − m − 2 2, 2 n m and q ∊ W − m 2, 2 n m, determines the potentials A and q in the set uniquely. The proof is based on a Carleman estimate with linear weights and with a gain of two derivatives and on the property of products of functions in Sobolev spaces.