3 years ago

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

Nikos Katzourakis

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.

Publisher URL: http://arxiv.org/abs/1811.02845

DOI: arXiv:1811.02845v2

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