Beilinson-Flach elements, Stark units and p-adic iterated integrals

We study weight one specializations of the Euler system of Beilinson-Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in suitable number fields to special values of the Hida-Rankin p-adic L-function. We show that the latter conjecture follows from expected properties of Beilinson-Flach elements and prove the analogue of the main theorem of Castella and Hsieh about generalized Kato classes.