Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (4): 572-576.

• Articles • Previous Articles    

THE OPIAL INEQUALITY IN RN

 DENG Yin-Bin   

  1. College of Mathematical and Statistics Science, Wuhan University, Wuhan 430072, China
  • Online:2001-10-06 Published:2001-10-06
  • Supported by:

    The research supported by Natural Science Fundation of China and the Excellent Teachers Fundation of Ministry of Education of China

Abstract:

This paper discusses the minimal eigenvalue 1(p, q,) and its best estimate of the following nonlinear eigenvalue problem −pu = |u|q−2 u, u|@
 = 0. Where   is a bounded smooth domain in RN,p is the p-laplace operator, p  2, q 2 [p, Np N−p ). By this result, the famous Opial inequality in RN are deduced

Key words: Opial inequality, eigenvalue, p-laplace

CLC Number: 

  • 35J10
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