Local behavior of the equilibrium measure under an external field non differentiable at a point

The equilibrium measure, μμ, associated with an external field, φφ, defined on Σ⊂RΣ⊂R and such that there exists a point x0x0 and an open interval, II, with x0∈I⊂Σx0∈I⊂Σ, φφ being continuous in II but analytic in I∖{x0}I∖{x0}, is studied. It is shown that the main asymptotic term of the derivatives of φφ at both sides of x0x0 determines the local behavior of Supp(μ) and the local behavior of the density associated with μμ. Some results related to a “forbidden region” for Supp(μ) are obtained. Also the behavior of the density associated with μμ is obtained when x0x0 is contained in the interior of the support.