H^s versus C^0-weighted minimizers
  We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology. 
Antonio Iannizzotto, Sunra Mosconi, Marco Squassina
math.AP