The output least squares identifiability of the diffusion coefficient from an H 1 -observation in a 2-D elliptic equation
ESAIM: Control, Optimisation and Calculus of Variations, Volume 8  (2002), p. 423-440

Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.

DOI : https://doi.org/10.1051/cocv:2002028
Classification:  62G05,  35R30,  93E24
Keywords: parameter estimation, diffusion coefficient, inverse problem, identifiability, least squares
@article{COCV_2002__8__423_0,
     author = {Chavent, Guy and Kunisch, Karl},
     title = {The output least squares identifiability of the diffusion coefficient from an $H^1$-observation in a 2-D elliptic equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     pages = {423-440},
     doi = {10.1051/cocv:2002028},
     zbl = {1092.93042},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__423_0}
}
Chavent, Guy; Kunisch, Karl. The output least squares identifiability of the diffusion coefficient from an $H^1$-observation in a 2-D elliptic equation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) , pp. 423-440. doi : 10.1051/cocv:2002028. http://www.numdam.org/item/COCV_2002__8__423_0/

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