  The validity of Weyl's law for the Steklov problem on domains with Lipschitz
boundaries is a well-known open question in spectral geometry. We answer this
question in two dimensions and show that Weyl's law holds for an even larger
class of surfaces with rough boundaries. This class includes domains with
interior cusps as well as 'slow' exterior cusps. Moreover, the condition on the
speed of exterior cusps cannot be improved, which makes our result in a sense
optimal. The proof is based on the methods of Suslina and Agranovich combined
with some observations about the boundary behaviour of conformal mappings.
