Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems
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Publication:3298394
DOI10.1088/1361-6420/AB8449zbMATH Open1487.65060arXiv1910.11595OpenAlexW3013617925MaRDI QIDQ3298394
Author name not available (Why is that?)
Publication date: 14 July 2020
Published in: (Search for Journal in Brave)
Abstract: We shall study in this paper the Lipschitz type stabilities and convergence rates of Tikhonov regularization for the recovery of the radiativities in elliptic and parabolic systems with Dirichlet boundary conditions. The Lipschitz type stability estimates are derived. Due to the difficulty of the verification of the existing source conditions or nonlinearity conditions for the considered inverse radiativity problems in high dimensional spaces, some new variational source conditions are proposed. The conditions are rigorously verified in general dimensional spaces under the Lipschitz type stability estimates and the reasonable convergence rates are achieved.
Full work available at URL: https://arxiv.org/abs/1910.11595
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