Increasing stability for the diffusion equation (Q2874809)

An elliptic PDE with Dirichlet boundary condition arising from tomographic problems is considered, along with an associated `Dirichlet-to-Neumann' or `voltage-to-current' map that gives the boundary measurements. With the corresponding inverse problem in mind, the equation is first transformed into a Helmholtz-type equation and stability estimates are established for the solution thereof in terms of the problem data, viz. the absorption and diffusion coefficients. These bounds suggest that the stability with respect to these coefficients improves with increasing frequency.