Determination of density of elliptic potential

In this paper, using techniques of finding boundary conditions for the volume (Newton) potential, we obtain the boundary conditions for the volume potential
$$ u(x)=\int_\Omega\varepsilon(x,\xi)\rho(\xi)d\xi, $$
where $\varepsilon(x,\xi)$ is the fundamental solution of the following elliptic equation
$$ L(x,D)\varepsilon(x,\xi)=-\sum_{i,j=1}^n\frac{\partial}{\partial x_i}a_{ij}(x)\frac{\partial}{\partial x_j}\varepsilon(x,\xi)+a(x)\varepsilon(x,\xi)=\delta(x,\xi). $$
Using the explicit boundary conditions for the potential $u(x)$, the density $\rho(x)$ of this potential is uniquely determined. Also, the inverse Sommerfeld problem for the Helmholtz equation is considered.