Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

Article type: Research Article

Authors: Alessandrini, Giovanni^{a; *} | de Hoop, Maarten V.^b | Gaburro, Romina^c | Sincich, Eva^a

Affiliations: [a] Dipartimento di Matematica e Geoscienze, Università di Trieste, Italy. E-mails: alessang@units.it, esincich@units.it | [b] Departments of Computational and Applied Mathematics, Earth Science, Rice University, Houston, Texas, USA. E-mail: mdehoop@rice.edu | [c] Department of Mathematics and Statistics, University of Limerick, Ireland. E-mail: romina.gaburro@ul.ie

Correspondence: [*] Corresponding author. E-mail: alessang@units.it.

Abstract: We consider the inverse boundary value problem of determining the potential q in the equation Δu+qu=0 in Ω⊂Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n⩾3 for potentials that are piecewise linear on a given partition of Ω. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation Δu+k2c−2u=0 at fixed frequency k.

Keywords: Lipschitz stability, Cauchy data, Green’s function, Full Waveform Inversion

DOI: 10.3233/ASY-171457

Journal: Asymptotic Analysis, vol. 108, no. 3, pp. 115-149, 2018