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We prove a global fractional differentiability result via the fractionalCaccioppoli-type estimate for solutions to nonlinear elliptic problems withmeasure data. This work is in fact inspired by the recent paper [B. Avelin, T.Kuusi, G. Mingione, {\em Nonlinear Calder\'on-Zygmund theory in the limitingcase}, Arch. Rational. Mech. Anal. {\bf 227}(2018), 663--714], that was devotedto the local fractional regularity for the solutions to nonlinear ellipticequations with right-hand side measure, of type $-\mathrm{div}\,\mathcal{A}(\nabla u) = \mu$ in the limiting case. Being a contribution torecent results of identifying function classes that solutions to such problemscould be defined, our aim in this work is to establish a global regularityresult in a setting of weighted fractional Sobolev spaces, where the weightsare powers of the distance function to the boundary of the smooth domains.

A global fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data