We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order , with . We consider the class of nonlocal operators , which consists of infinitesimal generators of stable Lévy processes belonging to the class of Caffarelli–Silvestre. For fully nonlinear operators elliptic with respect to , we prove that solutions to in , in , satisfy , where is the distance to and . We expect the class to be the largest scale-invariant subclass of for which this result is true. In this direction, we show that the class is too large for all solutions to behave as . The constants in all the estimates in this article remain bounded as the order of the equation approaches . Thus, in the limit , we recover the celebrated boundary regularity result due to Krylov for fully nonlinear elliptic equations.
"Boundary regularity for fully nonlinear integro-differential equations." Duke Math. J. 165 (11) 2079 - 2154, 15 August 2016. https://doi.org/10.1215/00127094-3476700