We investigate the support of the equilibrium measure associated with a cla
ss of nonconvex, nonsmooth external fields on a finite interval. Such equil
ibrium measures play an important role in various branches of analysis. In
this paper we obtain a sufficient condition which ensures that the support
consists of at most two intervals. This is applied to external fields of th
e form -c sign( x)|x|(alpha) with c > 0, alpha greater than or equal to 1 a
nd x is an element of [-1, 1]. If alpha is an odd integer, these external f
ields are smooth, and for this case the support was studied before by Deift
, Kriecherbauer and McLaughlin, and by Damelin and Kuijlaars.