论文标题
在某些部分数据上，Calderón类型的问题与边界条件混合条件
On some partial data Calderón type problems with mixed boundary conditions
论文作者
论文摘要
在本文中，我们考虑了（退化）椭圆方程建模（退化）在具有无法访问边界的介质中同时恢复体积和边界电位。这连接了本地和非局部calderón类型问题。我们证明了这类问题的两个主要结果：一方面，我们得出同时散装和边界跑步近似结果。在这些基础上，我们推断出局部散装和边界电位的独特性。另一方面，我们构建了与相应方程相关的CGO解决方案系列。这些使我们能够推断出任意界限的独特结果，而不一定是本地化的散装和边界电位。 CGO解决方案是通过二元性来构建的，对新的卡尔曼估计。
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. The CGO solutions are constructed by duality to a new Carleman estimate.
