The Calderón problem with partial data for conductivities with $3/2$ derivatives

Abstract

We extend a global uniqueness result for the Calderón problem with partial data, due to Kenig-Sjöstrand-Uhlmann, to the case of less regular conductivities. Specifically, we show that in dimensions $n\ge 3$, the knowledge of the Diricihlet-to-Neumann map, measured on possibly very small subsets of the boundary, determines uniquely a conductivity having essentially $3/2$ derivatives in an $L^2$ sense.

References in corpus (3)

• Global uniqueness for the Calderón problem with Lipschitz conductivities
• Uniqueness in Calderón's problem for conductivities with unbounded gradient
• Local analytic regularity in the linearized Calderón problem

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