An $L^\infty$ Regularization Strategy to the Inverse Source Identification Problem for Elliptic Equations

Abstract

In this paper we utilize new methods of calculus of variations in $L^\infty$ to provide a regularization strategy to the ill-posed inverse problem of identifying the source of a nonhomogeneous linear elliptic equation, satisfying Dirichlet data on a domain. One of the advantages over the classical Tykhonov regularization in $L^2$ is that the approximated solution of the PDE is uniformly close to the noisy measurements taken on a compact subset of the domain.