Global H\"older regularity for the fractional $p$-Laplacian
  By virtue of barrier arguments we prove $C^\alpha$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ($p<2$) of degenerate ($p>2$) case. 
Antonio Iannizzotto, Sunra Mosconi, Marco Squassina
math.AP