Gradient Estimates for p-Laplacian Lichnerowicz Equation on Noncompact Metric Measure Space

Abstract

In this paper, the authors obtain the gradient estimates for positive solutions to the weighted p-Laplacian Lichnerowicz equation ${\Delta _{p,f}}u + c{u^\sigma } = 0$ on noncompact smooth metric measure space, where c is a nonnegative constant, and p, σ (1 < p ≤ 2, σ ≤ p - 1) are real constants. Moreover, by the gradient estimate, they can get the corresponding Liouville theorem and Harnack inequality.

Keywords

p-Laplacian / Positive solutions / Liouville theorem

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