The support of the equilibrium measure for a class of external fields on afinite interval

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.