  In this paper, we define a two-variable analogue of Perrin-Riou's p-adic
regulator map for the Iwasawa cohomology of a crystalline representation of the
absolute Galois group of $\mathbf{Q}_p$, over a Galois extension of
$\mathbf{Q}_p$ whose Galois group is an abelian p-adic Lie group of dimension
2.
  We use this regulator map to study p-adic representations of global Galois
groups over certain abelian extensions of number fields whose localisation at
the primes above p are extensions of the above type. In the example of the
restriction to an imaginary quadratic field of the representation attached to a
modular form, we formulate a conjecture on the existence of a "zeta element",
whose image under the regulator map is a p-adic L-function. We show that this
conjecture implies the known properties of the 2-variable p-adic L-functions
constructed by Perrin-Riou and Kim.
