We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose inaccessible portion of the boundary is contained in a hyperplane, and we are given the Cauchy data set on the complement. The uniqueness and logarithmic stability for this problem were established in [37] and [7], respectively. We establish stability estimates in the high frequency regime, with an explicit dependence on the frequency parameter, under mild regularity assumptions on the potentials, sharpening those of [7].

中文翻译：

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双谐波算子在高频下的部分数据逆边值问题的稳定性估计

我们从部分柯西数据集的知识出发，研究了确定的Helmholtz型方程中被干扰的双谐波算子的势的逆边界值问题。我们的几何设置是一个域，其边界的不可访问部分包含在一个超平面中，并且我们在补数上获得了柯西数据集。此问题的唯一性和对数稳定性在[37]和[7]， 分别。我们在电位的适度规律性假设下，在高频范围内建立稳定估计，并明确依赖频率参数，从而提高[7]。