Local gradient estimate for p-harmonic functions on Riemannian manifolds

By Xiaodong Wang, Lei Zhang. 2010

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For positive p-harmonic functions on Riemannian mani- folds, we derive a gradient estimate and Harnack inequality with con- stants 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 de- fined. Our approach is based on a careful application of the Moser iter- ation 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eddcbf2d1f248800726651722a16c0775bd62705