An L∞ regularisation strategy to the inverse source identification problem for elliptic equationsKatzourakis, N. (2019) An L∞ regularisation strategy to the inverse source identification problem for elliptic equations. SIAM Journal on Mathematical Analysis (SIMA), 51 (2). pp. 1349-1370. ISSN 0036-1410
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1137/18M1226373 Abstract/SummaryIn this paper we utilise new methods of Calculus of Variations in L ∞ 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.
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