Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality

Abstract

The authors prove Carleman estimates for the Schrödinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining L ^p-potentials. An L ²-level observability inequality and unique continuation results for the Schrödinger equation are also obtained.

Keywords

Schrödinger equation / Carleman estimate / Observability inequality / Inverse problem / Unique continuation

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