Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (3): 481-492.

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The Gradient Estimates of Laplace Equations with Oblique Boundary Value Problem

Xiang Ni1, Shi Juhua1, Xu Jinju2, Wu Yan1   

  1. 1 Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062;
    2 Department of Mathematics, Shanghai University, Shanghai 200444
  • Received:2015-09-14 Revised:2016-03-14 Online:2016-06-26 Published:2016-06-26
  • Supported by:

    Supported by the NSFC (11101132), the Foundation of Hubei Provincial Department of Education (Q20120105) and the Opening Practicle Teaching System Study for the Partial Differential Equations of Innovative Thinking Guide

Abstract:

In this paper, the authors study two proofs for the gradient estimates of the Laplace equations with oblique boundary value condition. For the first proof, the gradient estimates of Lieberman[1] are rearranged; for the second proof, barrier function which is different from [1] is used to obtain the gradient estimates. They both use the property of the maximum value point, and get the near boundary gradient estimates and boundary gradient estimates, combining the given inner gradient estimates in [2], and then they obtain the global gradient estimates.

Key words: Laplace equations, Oblique boundary value problem, Gradient estimates

CLC Number: 

  • O175.2
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