Two-point determination conjecture for planar permeability

Let $D\subseteq\mathbb{C}$ be a fluid domain with a permeability function $\lambda\in C^\infty(\overline{D})$, and let $g_w$ and $g_\xi$ be Green functions for the operator $\nabla\lambda\nabla$ with distinct points $w,\xi\in D$. The corresponding boundary velocity profiles are $\lambda\partial_n g_w$ and $\lambda\partial_n g_\xi$.

Two-point determination conjecture. If both

$$\lambda\partial_n g_w\quad\text{and}\quad\lambda\partial_n g_\xi$$

are known for distinct points $w,\xi\in D$, then $\lambda$ can be determined.

This is a finite-data inverse problem related to Calderón's problem. The source notes that the response at a single point cannot detect the permeability, while it leaves open whether responses at two or finitely many points suffice.