Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

We study the inverse problem in Optical Tomography of determining the optical properties of a medium Ω⊂ℝn, with n≥ 3, under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency ω=k/c, where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient μa at the boundary ∂Ω in terms of the measurements in the case when the scattering coefficient μs is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on μa, μs.