Work

A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements

Year: 2026

Type: article

Abstract: We consider the inverse boundary value problem of the simultaneous determination of the coefficients $$\sigma $$ σ and q of the equation $$-\text{ div }(\sigma \nabla u)+qu = 0$$ - div ( σ ∇ u ) + q u = 0 from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion $$\Sigma $$ Σ of the boundary $$\partial \Omega $$ ∂ Ω of a domain $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n , with $$n\ge 3$$ n ≥ 3 . We assume that $$\sigma $$ σ and q are a-priori known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of $$\Omega $$ Ω with curved interfaces. We prove that $$\sigma $$ σ and q can be uniquely determined in $$\Omega $$ Ω from the knowledge of the local map.

Source: Annali di Matematica Pura ed Applicata (1923 -)

DOI: 10.1007/s10231-026-01686-0

Authors: Niall Donlon, Romina Gaburro

Institution: University of Limerick

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Engineering and Physical Sciences Research Council