  We discuss 1/2 BPS domain walls in the 3d $\mathcal N=4$ supersymmetric gauge
theory which is self-dual under the 3d mirror symmetry. We find that if a
BF-type coupling is introduced, invariance of the BPS domain wall under the
duality transformation can be explicitly seen from the classical BPS equations.
It has been known that particles and vortices are swapped under the 3d duality
transformations. We show that Noether charges and vortex topological charges
localized on the domain walls are correctly exchanged under the 3d mirror
symmetry.
