In this paper, we develop a general approach to prove stability for the nonlinear second step of hybrid inverse problems with one internal measurement. We work with general functionals of the form F = σ|?u|p, 0 < p≤ 1, where u is the solution of the elliptic partial differential equation ? · σ?u = 0 on a bounded domain ? with boundary conditions u|?? = f. In the case p = 1 this problem has application to current density impedance imaging, where F = σ|?u| represents the magnitude of the current density field. We prove stability of the linearization and H?lder conditional stability for the nonlinear problem of recovering σ from one internal measurement.
展开▼
