Nontangential a.e. vanishing of the oblique derivative of a harmonic function with respect to a Hölder continuous vector field on a Lipschitz boundary is shown to imply that the harmonic function is constant.
"Nonvariational layer potentials with respect to Hölder continuous vector fields." Rev. Mat. Iberoamericana 23 (1) 201 - 212, April, 2007.