A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with   Lipschitz Boundary Values
  In this note we show that gradient of Harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in $L^p$ for all finite $p\geq 1$. 
Nikos Katzourakis (Reading, UK)
math.AP