Convex source support in half-plane

摘要

This work extends the concept of convex source support to the framework of inverse source problems for the Poisson equation in an insulated upper half-plane. The convex source support is, in essence, the smallest (nonempty) convex set that supports a source that produces the measured (nontrivial) data on the horizontal axis. In particular, it belongs to the convex hull of the support of any source that is compatible with the measurements. We modify a previously introduced method for reconstructing the convex source support in bounded domains to our unbounded setting. The performance of the resulting numerical algorithm is analyzed both for the inverse source problem and for electrical impedance tomography with single pair of boundary current and potential as the measurement data.