Title:
On the Inverse Source Identification Problem in L∞ for Fully Nonlinear Elliptic PDE
Author(s):
Ayanbayev, Birzhan; Katzourakis, Nikos
Year of publication:
2021
Available Date:
2021-09-09T06:35:44Z
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.
Part of Identifier:
e-ISSN (online): 2305-2228
Keywords:
Regularisation strategy
Tykhonov regularisation
Inverse source identification problem
Fully nonlinear elliptic equations
Calculus of Variations in L∞
DDC-Classification:
510 Mathematik
Publication Type:
Wissenschaftlicher Artikel
URL of the Original Publication:
DOI of the Original Publication:
Journaltitle:
Vietnam Journal of Mathematics
Department/institution:
Mathematik und Informatik
Institut für Mathematik