Work

Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator

Year: 2026

Type: article

Abstract: We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator ( − Δ ) m with m ⩾ 2 . We show that the map from the coefficients to a certain bilinear form is injective. We have a particular focus on obtaining these results under lower regularity on the coefficients. It is known that knowledge of this bilinear form is equivalent to a knowledge of a Dirichlet to Neumann map or the Cauchy data for solutions.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ae73ac

Authors: R M Brown, D Faraco, L D Gauthier

Institutions: University of Kentucky, Institute of Mathematical Sciences, Carthage College

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Simons Foundation, Comunidad de Madrid, Agencia Estatal de Investigación, H2020 European Research Council