Local gradient estimate for p-harmonic functions on Riemannian manifolds

For positive p-harmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension n, p and the radius of the ball on which the function is defined. Our approach is based on a careful application of the Moser iteration technique and is different from Cheng-Yau's method 2 employed by Kostchwar and Ni 5, in which a gradient estimate for positive p-harmonic functions is derived under the assumption that the sectional curvature is bounded from below.