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.
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Gregory C. Verchota, Nonvariational layer potentials with respect to H¨older continuous vector fields. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 201–212