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Boundary determination from local boundary data for a fractional Calderón problem
[Submitted on 23 Jun 2026] · 2026-06-25 · via math updates on arXiv.org

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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, for a generic fractional exponent, 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.

Submission history

From: Heiko Gimperlein [view email]
[v1] Tue, 23 Jun 2026 18:01:48 UTC (15 KB)

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