Local gradient estimate for p-harmonic functionson Riemannian manifolds

摘要

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 func-tion 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 gradi-ent estimate for positive p-harmonic functions is derived under the assumption that the sectional curvature is bounded from below.