An $L^\infty$ regularisation strategy to the inverse source identification problem for elliptic equations

Nikos Katzourakis

An $L^\infty$ regularisation strategy to the inverse source identification problem for elliptic equations

Analysis of PDEs 2019-01-17 v3

Authors: Nikos Katzourakis

Abstract

In this paper we utilise new methods of Calculus of Variations in $L^\infty$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet data on a domain. One of the advantages over the classical Tykhonov regularisation 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.

Keywords

tikhonov regularization regularity for elliptic equations dirichlet problem

Cite

@article{arxiv.1811.02845,
  title  = {An $L^\infty$ regularisation strategy to the inverse source identification problem for elliptic equations},
  author = {Nikos Katzourakis},
  journal= {arXiv preprint arXiv:1811.02845},
  year   = {2019}
}