We study N = 2 supersymmetric Born-Infeld-Higgs theory in three dimens
ions and derive Bogomol'nyi relations in its bosonic sector. A peculia
r coupling between the Higgs and the gauge field (with dynamics determ
ined by the Born-Infeld action) is forced by supersymmetry. The result
ing equations coincide with those arising in the Maxwell-Higgs model.
Concerning Bogomol'nyi bounds for the vortex energy, they are derived
from the N = 2 supersymmetry algebra. (C) 1998 Elsevier Science B.V.