Journal of East China Normal University(Natural Sc ›› 2010, Vol. 2010 ›› Issue (1): 91-98.

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Sharp estimate of the p-Laplace operator

WANG Lin-feng   

  1. School of Science, Nantong University, Nantong Jiangsu226000, China
  • Received:2009-02-02 Revised:2009-05-07 Online:2010-01-25 Published:2010-01-25
  • Contact: WANG Lin-feng

Abstract: Let M be an n-dimensional complete noncompact Riemannian manifold with metric g, triangle_p(1<pleqslant 2) the p-Laplace operator, by using the classical method of Li-Yau, a gradient estimate of the positive solution to equation triangle_pu=-lambda |u|^p-2u was proved under suitable curvature condition, in which lambdageqslant 0 is a constant; the upper bound estimate of lambda was a byproduct; one also showed that this estimate is sharp. This result generalizes the gradient estimate of the positive solution to elliptic equation triangle u=-lambda

Key words: gradient estimate, sharp estimate, p-Laplace operator, gradient estimate, sharp estimate

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