On the geometric structures of transmission eigenfunctions with a conductive boundary condition and applications

Determining a Piecewise Conductive Medium Body by a Single Far-Field Measurement

“…Hence, it is unpractical to consider the inverse problem in the generic case. Nevertheless, for the inverse problem (1.13), it is proved in [22] that if Ω is a convex polygon, then Ω and λ can be uniquely determined independent of a generic variable q. Compared to our study in [22], there are two interesting and significant extensions in the current work.…”

“…Nevertheless, for the inverse problem (1.13), it is proved in [22] that if Ω is a convex polygon, then Ω and λ can be uniquely determined independent of a generic variable q. Compared to our study in [22], there are two interesting and significant extensions in the current work. First, in addition to the support Ω and the boundary conductive parameter λ of the medium body, we shall further determine the material parameter inside the body, i.e.…”

“…q. Moreover, we develop technical tricks that can handle more general conductive parameter λ than that was considered in [22]. Second, we consider a more complicated physical setup than that in [22].…”

“…Moreover, we develop technical tricks that can handle more general conductive parameter λ than that was considered in [22]. Second, we consider a more complicated physical setup than that in [22]. For example, we may allow the presence of multiple conductive interfaces that are embedded in a layered medium, and this shall be more evident in Section 2.…”

“…We shall also need to make use of the following complex geometric optics (CGO) solution whose logarithm is a branch of the square root stated in the following lemma to prove our main results (cf. [4,22]).…”