An inverse problem for the relativistic Schrödinger equation with partial boundary data. Issue 11 (17th August 2020) - Krishnan, Venkateswaran P.; Vashisth, Manmohan
ABSTRACT: We study the inverse problem of determining the vector and scalar potentials A = ( A 0 ( t, x ), A 1 ( t, x ), …, A n ( t, x ) ) and q ( t, x ), respectively, in the relativistic Schrödinger equation ∂ t + A 0 ( t, x ) 2 − ∑ j = 1 n ∂ j + A j ( t, x ) 2 + q ( t, x ) u ( t, x ) = 0 in the region Q = ( 0, T ) × Ω, where Ω is a C 2 bounded domain in R n for n ≥ 3 and T > diam ( Ω ) from partial data on the boundary ∂ Q . We prove the unique determination of these potentials modulo a natural gauge invariance for the vector field term.