Abstract:In this article, we introduce a model featuring a Lévy process in a bounded domain with semi-transparent boundary, by considering the fractional Laplacian operator with lower order non-local perturbations. We study the wellposedness of the model, certain qualitative properties and Runge type approximation. Furthermore, we consider the inverse problem of determining the unknown coefficients in our model from the exterior measurements of the corresponding Cauchy data. We also discuss the recovery of all the unknown coefficients from a single measurement.

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中文翻译：

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具有低阶非局部摄动的分数-拉普拉斯算子的反问题

摘要：在本文中，我们通过考虑具有低阶非局部摄动的分数阶Laplacian算子，介绍了一个具有半透明边界的有界域中的Lévy过程的模型。我们研究了模型的适定性，某些定性性质和Runge类型逼近。此外，我们考虑从相应柯西数据的外部测量结果确定模型中未知系数的反问题。我们还将讨论从一次测量中所有未知系数的恢复。

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