  Strain and rotation fields of dislocations in monolayer graphene have been
mapped in a recent experiment. These fields are finite everywhere and differ
from those given by linear elasticity which does not consider rotation
explicitly and predicts infinite rotation and strains at the dislocation point.
A derivative regularization of two-dimensional linear elasticity fixes these
shortcomings. The theory adds rotation, dislocation and residual strain
energies to the usual elastic energy. There are two extra material constants
that determine the size of the dislocation core and are determined from
experimental data. These findings are useful for studies of dislocations in
graphene and for analyzing incipient plasticity in two dimensional crystals.
