We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of Hölder type. For sake of simplicity, we limited our study to the class of Helmholtz equations \(\Delta + V\) with bounded potential V.

中文翻译：

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具有内部数据的逆介质问题的Hölder稳定性

我们对内部数据的逆介质问题感兴趣。这个问题源于多波成像。我们在当前工作中旨在根据边界条件研究反演的适定性。我们精确地表明，我们实际上具有Hölder类型的稳定性估计。为简单起见，我们将研究限制在具有势能V的Helmholtz方程\（\ Delta + V \）的类别中。