Harnack inequality and regularity of p-Laplace equation on complete manifolds

Abstract

In this paper, we will derive a mean value inequality and a Harnack inequality for nonnegative functions which satisfies the differential inequality
|div(|f|^p−2∇f)|≤A   f^p−1
in the weak sence on complete manifolds, where constants A≥0, p>1; as a consequence, we give a C^α estimate for weak solutions of the above differential inequality, then we generalize the results in [1], [2].
We would thank Professor Z. G. Bai and Professor Y. B. Shen for their long time encourgement, we also thank the referee for invaluable comments.