On the inverse source identification problem in L ∞ for fully nonlinear elliptic PDE

Ayanbayev, B. and Katzourakis, N. (2021) On the inverse source identification problem in L ∞ for fully nonlinear elliptic PDE. Vietnam Journal of Mathematics, 49 (3). pp. 815-829. ISSN 2305-221X doi: 10.1007/s10013-021-00515-6

Abstract/Summary

Abstract: In this paper we generalise the results proved in N. Katzourakis (SIAM J. Math. Anal. 51, 1349–1370, 2019) by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator. We deal with the highly nonlinear nonconvex nature of the problem and the lack of weak continuity by introducing a two-parameter Tykhonov regularisation with a higher order L2 “viscosity term” for the L∞ minimisation problem which allows to approximate by weakly lower semicontinuous cost functionals.

Item Type	Article
URI	https://reading-pure-test.eprints-hosting.org/id/eprint/99741
Identification Number/DOI	10.1007/s10013-021-00515-6
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Central Services
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