The Output Least Squares Identifiability of the Diffusion Coefficient from an H 1 –Observation in a 2–D Elliptic Equation

Output least squares stability for the diusion coecient in an elliptic equation in dimen- sion 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. Mathematics Subject Classication. 62G05, 35R30, 93E24.

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