In this article we prove that the singular set of Dirichlet-minimizing Q-valued functions is countably .m2/-rectifiable and we give upper bounds for the .m2/-dimensional Minkowski content of the set of singular points with multiplicity Q.
Building upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125-184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in Rn+1 with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null Hn-1 measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E.
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