  We show that the Hawking--Penrose singularity theorem, and the generalisation
of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian
metrics that are of $C^{1, 1}$-regularity. We formulate appropriate weak
versions of the strong energy condition and genericity condition for
$C^{1,1}$-metrics, and of $C^0$-trapped submanifolds. By regularisation, we
show that, under these weak conditions, causal geodesics necessarily become
non-maximising. This requires a detailed analysis of the matrix Riccati
equation for the approximating metrics, which may be of independent interest.
