Reconstructing the right-hand side of a Poisson equation with random noise

Abstract. An inverse source problem for the Poisson equation is looked at in this article. This is a problem that is poorly posed because even minor changes in the data can result in arbitrarily large changes in the results. We first demonstrate some useful lemmas about our proposed problem before presenting the main results. Then, at that point, we propose a regularization strategy to manage the reverse source issue and get a union rate with random noise