A global fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data
Volume 263 / 2022
Abstract
We prove a global fractional differentiability result via the fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data. This work is inspired by the recent paper [B. Avelin, T. Kuusi and G. Mingione, Arch. Ration. Mech. Anal. {227} (2018), 663–714], devoted to the local fractional regularity for solutions to nonlinear elliptic equations with measure right-hand side, of type $-\mathrm {div}\, \mathcal {A}(\nabla u) = \mu $ in the limiting case. Being a contribution to recent results of identifying function classes in which solutions to such problems could be defined, our aim is to establish a global regularity result in weighted fractional Sobolev spaces, where the weights are powers of the distance function to the boundary of the smooth domain.
