(untitled) (Journal of Partial Differential Equations, 2023)
We consider a parameter identification problem associated with a quasilinear elliptic Neumann boundary value problem involving a parameter function a(·) and the solution u(·), where the problem is to identify a(·) on an interval I:=g(Γ) from the knowledge of the solution u(·) as g on Γ, where Γ is a given curve on the boundary of the domain Ω⊆R^3 of the problem and g is a continuous function. The inverse problem is formulated as a problem of solving an operator equation involving a compact operator depending on the data, and for obtaining stable approximate solutions under noisy data, a new regularization method is considered. The derived error estimates are similar to, and in certain cases better than, the classical Tikhonov regularization considered in the literature in recent past.