Local uniqueness for an inverse boundary value problem with partial data

Abstract

In dimension n ≥ 3 n\geq 3 , we prove a local uniqueness result for the potentials q q of the Schrödinger equation − Δ u + q u = 0 -\Delta u+qu=0 from partial boundary data. More precisely, we show that potentials q 1 , q 2 ∈ L ∞ q_1,q_2\in L^\infty with positive essential infima can be distinguished by local boundary data if there is a neighborhood of a boundary part where q 1 ≥ q 2 q_1\geq q_2 and q 1 ≢ q 2 q_1\not \equiv q_2 .