Unique Continuation, Runge Approximation and the Fractional Calderón Problem

Abstract

In these notes for the proceedings of the “Journée Équations aux Dérivées Partielles”, we survey some of the recent progress in and the interplay of unique continuation, approximation and some related nonlocal inverse problems. In particular, we discuss the qualitative and quantitative global unique continuation properties of the fractional Laplacian and its Runge approximation properties. We explain how this leads to surprising results on the inverse problems for the associated operators.

Locations

• Journées Équations aux dérivées partielles - View - PDF
• French digital mathematics library (Numdam) - View - PDF