Remarks on Local Boundedness and Local H\"older Continuity of Local Weak   Solutions to Anisotropic $p$-Laplacian Type Equations
  Locally bounded, local weak solutions to a special class of quasilinear, anisotropic, $p$-Laplacian type elliptic equations, are shown to be locally H\"older continuous. Homogeneous local upper bounds are established for local weak solutions to a general class of quasilinear anisotropic equations. 
Emmanuele DiBenedetto, Ugo Gianazza, Vincenzo Vespri
math.AP