The obstacle problem for the infinity fractional laplacian

Abstract

Given g an α-H¨older continuous function defined on the boundary of a bounded domain Ω and given ψ a continuous obstacle defined in Ω, in this article, we find u an α-H¨older extension of g in Ω with u ≥ ψ. This function u minimizes the α-H¨older semi-norm of all possible extensions with these properties and it is a viscosity solution of the associated obstacle problem for the infinity fractional Laplace operator.