Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation

In this short note, we investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data. The main technique is based on higher order linearization and monotonicity approaches. With these methods at hand, we can determine the diffusion and absorption coefficients together with the shape of a cavity simultaneously by knowing the corresponding localized Dirichlet–Neumann operator.