  Parameter identification problems for partial differential equations are an
important subclass of inverse problems. The parameter-to-state map, which maps
the parameter of interest to the respective solution of the PDE or state of the
system, plays the central role in the (usually nonlinear) forward operator.
Consequently, one is interested in well-definedness and further analytic
properties such as continuity and differentiability of this operator w.r.t. the
parameter in order to make sure that techniques from inverse problems theory
may be successfully applied to solve the inverse problem. In this work, we
present a general functional analytic framework suited for the study of a huge
class of parameter identification problems including a variety of elliptic
boundary value problems (in divergence form) with Dirichlet, Neumann, Robin or
mixed boundary conditions. In particular, we show that the corresponding
parameter-to-state operators fulfil, under suitable conditions, the tangential
cone condition, which is often postulated for numerical solution techniques.
This framework particularly covers the inverse medium problem and an inverse
problem that arises in terahertz tomography.
