Pacific journal of mathematics vol:199 issue:2 pages:303-320
We investigate the support of the equilibrium measure associated with a class of nonconvex, nonsmooth external fields on a finite interval. Such equilibrium 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 the form -c sign( x)|x|(alpha) with c > 0, alpha greater than or equal to 1 and x is an element of [-1, 1]. If alpha is an odd integer, these external fields are smooth, and for this case the support was studied before by Deift, Kriecherbauer and McLaughlin, and by Damelin and Kuijlaars.