PUB - Publikationen an der Universität Bielefeld

The problem of interest in this article is to study the (non-local) inverse problem of recovering a potential based on the boundary measurement associated with the fractional Schrodinger equation. Let 0 < a < 1, and let u solve { ((-Delta)a +q)u = 0 in Omega, supp u subset of (Omega) over bar boolean OR (W) over bar, (W) over bar boolean AND (Omega) over bar = (sic). We show that, by making an exterior to boundary measurement as (u vertical bar W, u(x)/d(x)(a)vertical bar(Sigma) , it is possible to determine q uniquely in Omega, where Sigma subset of partial derivative Omega is a non-empty open subset and d(x) = d(x, partial derivative Omega) denotes the boundary distance function. We also discuss a local characterization of large a-harmonic functions in a ball or in the half space and its applications, which include boundary unique continuation and a local density result.