QUASI-LINEAR FRACTIONAL-ORDER OPERATORS IN LIPSCHITZ DOMAINS

We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional -order quasi -linear operators with variable coefficients on Lipschitz domains \Omega of R d . Our estimates are consistent with the boundary behavior of solutions on smooth domains and apply to fractional p-Laplacians and operators with finite horizon. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional p-Laplacians and present several simulations that reveal the boundary behavior of solutions.