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On (global) unique continuation properties of the fractional discrete Laplacian

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FD2W01 - Deterministic and stochastic fractional differential equations and jump processes

We present various qualitative and quantitative (global) unique continuation properties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation properties, the fractional discrete Laplacian does not enjoy these in general. While discretization thus counteracts the strong rigidity properties of the continuum fractional Laplacian, by discussing quantitative forms of unique continuation, we illustrate that these properties can be recovered if exponentially small (in the lattice size) correction terms are added. This in particular allows us to deduce stability properties for a discrete, linear inverse problem for the fractional Laplacian. Joint work with Aingeru Fernández-Bertolin and Angkana Rüland.

This talk is part of the Isaac Newton Institute Seminar Series series.

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