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arXiv · 2606.25044

Boundary determination from local boundary data for a fractional Calder\'{o}n problem

Heiko Gimperlein·Magnus Goffeng
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Abstract

We introduce a new Calder\'{o}n-type problem for fractional powers of Schr\"{o}dinger 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 Calder\'{o}n 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. 2026-06-23. Boundary determination from local boundary data for a fractional Calder\'{o}n problem. https://arxiv.org/abs/2606.25044

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