Stability of solutions for some inverse problems
Résumé
In this article we establish three stability results for some inverse problems. More precisely we consider the following boundary value problem: $\Delta u + \lambda u + \mu = 0$ in $\Omega$, $u = 0$ on $\partial\Omega$, where $\lambda$ and $\mu$ are real constants and $\Omega \subset \mathbb R^2$ is a smooth bounded simply-connected open set. The inverse problem consists in the identification of $\lambda$ and $\mu$ from knowledge of the normal flux $\partial u/\partial\nu$ on $\partial\Omega$ corresponding to some nontrivial solution.