https://www.researchgate.net/profile/Jesse-Railo
Thu, September 29, 2022, 9:00-10:00 am PDT via Zoom
Title: Inverse fractional conductivity problem.
Abstract: We discuss recent progress in inverse problems for elliptic nonlocal operators. The main focus is in the recovery of variable kernels of fractional order operators. We consider a model problem of a fractional conductivity equation with global coefficients. The problem has a rather rich mathematical theory and shares many similarities with the Calderón problem for the classical conductivity equation. Our work has this far established many nonlocal analogies of the classical results, including interior and exterior (analogous to boundary) uniqueness results with nondisjoint partial data, a construction of special solutions concentrating in the exterior (without UCP/Runge approximation), low regularity theory using a UCP result for the fractional Laplacians in L^p spaces with p = n/s > 2, counterexamples for partial data on disjoint sets, stability results, and some partial results for fully nonlinear, nonlocal, p-Laplacian type equations. Some of these results with main ideas will be presented.