A new regularization method for a parameter identification problem in a non-linear partial differential equation
We consider a parameter identification problem related to a quasi-linear elliptic Neumann boundary value problem involving a parameter function $a(\cdot)$ and the solution $u(\cdot)$, where the problem is to identify $a(\cdot)$ on an interval $I:= g(Γ)$ from the knowledge of the solution $u(\cdot)$ as $g$ on $Γ$, where $Γ$ is a given curve on the boundary of the domain $Ω\subseteq \mathbb{R}^3$ of the problem and $g$ is a continuous function. For obtaining stable approximate solutions, we consider new regularization method which gives error estimates similar to, and in certain cases better than, the classical Tikhonov regularization considered in the literature in recent past.
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