The Calderón problem for nonlocal operators
Abstract
We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into determining the coefficients from the boundary Cauchy data of the elliptic operator on the open set, the Calderón problem. As a corollary we establish several new results for nonlocal inverse problems by using the corresponding results for the local inverse problems. In particular the isotropic nonlocal Calderón problem can be resolved completely, assuming some regularity assumptions on the coefficients, and the anisotropic Calderón problem modulo an isometry which is the identity at the boundary for realanalytic anisotropic conductivities in dimension greater than two and bounded and measurable anisotropic conductivities in two dimensions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09265
 Bibcode:
 2021arXiv211009265G
 Keywords:

 Mathematics  Analysis of PDEs