Local uniqueness for an inverse boundary value problem with partial data

Abstract

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

References in corpus (3)

• Uniqueness in Calderon's problem with Lipschitz conductivities
• Monotonicity based shape reconstruction in electrical impedance tomography
• The Calderon problem with partial data on manifolds and applications

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