Identification of piecewise constant sources in non-homogeneous media based on boundary measurements

In this study, we consider the inverse problem of determining a source term in an elliptic problem based on boundary measurements. The boundary measurements allow the unique determination of the harmonic component of the source, and thus a priori information is required for its complete identification. Using this a priori information, we determine the compactness of the class of sources and a uniqueness theorem for its identification from Cauchy data, thereby allowing us to propose a stable algorithm for finding “approximate solutions” of the inverse problem. The proposed procedure is demonstrated by individual cases, where we know the “geometry” of the inner region and the source takes a constant value.