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GRADIENT ESTIMATES FOR THE p-LAPLACIAN LICHNEROWICZ EQUATION ON SMOOTH METRIC MEASURE SPACES

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Affiliation of Author(s):理学院

Title of Paper:GRADIENT ESTIMATES FOR THE p-LAPLACIAN LICHNEROWICZ EQUATION ON SMOOTH METRIC MEASURE SPACES

Journal:PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Key Words:p-Laplacian positive solutions gradient estimate

Abstract:In this paper, we consider the weighted p-Laplacian Lichnerowicz equation Delta(p,f) u + cu(sigma) = 0 on smooth metric measure spaces, where c >= 0, p > 1, and sigma <= p - 1 are real constants. A local gradient estimate for positive solutions to this equation is derived, and as applications, we give a corresponding Liouville property and Harnack inequality.

ISSN No.:0002-9939

Translation or Not:no

Date of Publication:2018-12-01

Co-author:Yang, Dengyun

Correspondence Author:zl

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