A sharp gradient estimate for the weighted p-Laplacian |
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Authors: | Lin-feng Wang Yue-ping Zhu |
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Institution: | 1. School of Science, Nantong University, Nantong, 226007, China
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Abstract: | Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, d?? = e h (x) dV (x) the weighted measure and ????,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation $$ \Delta _{\mu ,p} u = - \lambda _{\mu ,p} |u|^{p - 2} u $$ for p ?? (1, 2). We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem.. |
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Keywords: | weighted p-Laplacian gradient estimate Harnack inequality Liouville theorem |
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