Numerical procedure of determining of the supports of the equilibrium measures and sets of equilibrium in the extremal tasks of logarithmic potential theory

We present the procedures of determining of the supports of the equilibrium measures and sets of equilibrium which base on minimizing of some extremal functionals. We propose the method of finding set of equilibrium in case the support of the equilibrium measure $S_{\mu_Q^{x,\sigma}}$ and set $S_{\sigma-\mu_Q^{x,\sigma}}$, where a constraint is not hit are intervals. As examples we discussed a contact problem in elasticity and zero asymptotics of Krawtchouk polynomials.