Goncharov, A.2016-02-082016-02-0820141331-4343http://hdl.handle.net/11693/26664By means of weakly equilibrium Cantor-type sets, solutions of two problems related to polynomial inequalities are presented: the problem by M. Baran et al. about a compact set K ⊂ double-struck C such that the Markov inequality is not valid on K with the best Markov's exponent, and the problem by L. Frerick et al. concerning compact sets satisfying the local form of Markov's inequality with a given exponent, but not satisfying the global version of Markov's inequality with the same parameter. © ELEMENT.EnglishGlobal and local Markov's inequalitiesMarkov's exponents.Article10.7153/mia-17-111