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arXiv · 2606.25044

Boundary determination from local boundary data for a fractional Calderón problem

Heiko Gimperlein·Magnus Goffeng
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Abstract

We introduce a new Calderón-type problem for fractional powers of Schrödinger operators, with local boundary conditions. The associated Dirichlet-to-Neumann operator maps Dirichlet data to Neumann data on the boundary. We show that this operator determines the Taylor series of the potential at the boundary. In particular, analytic potentials are uniquely determined. These are the first results for a fractional Calderón problem with sources and measurements on the boundary. Our proof builds on recent advances for pseudodifferential boundary value problems to compute the complete symbol of the Dirichlet-to-Neumann operator.

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Heiko Gimperlein, Magnus Goffeng. 2026-08-24. Boundary determination from local boundary data for a fractional Calderón problem. https://arxiv.org/abs/2606.25044

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