数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (1): 75-81.

• 论文 • 上一篇    下一篇

L∞ ESTIMATE FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN RN

李工宝   

  1. Inst. of Math. Sci., The Chinese Academy of Sciences Sinica, PO Box 71007, Wuhan 470071, China
  • 收稿日期:1992-03-10 出版日期:1994-03-25 发布日期:1994-03-25
  • 基金资助:
    Supported by the Youth Foundation of NSFC.

L∞ ESTIMATE FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN RN

Li Gongbao   

  1. Inst. of Math. Sci., The Chinese Academy of Sciences Sinica, PO Box 71007, Wuhan 470071, China
  • Received:1992-03-10 Online:1994-03-25 Published:1994-03-25
  • Supported by:
    Supported by the Youth Foundation of NSFC.

PDF (PC)

37

摘要： In this paper, we get the L∞ estimate for the solutions of the following elliptic equation in RN with limiting Sobolev exponent and inhomogeneous term
-∑i=1N(∂)/∂xi(|▽u|p-2(∂u)/∂xi)+c(x)|u|p-2u=f(x,u)+g(x),u∈RN,u∈W1,p(RN),N > p > 1 and we show that any solution u of the above equation satisfies
||u||∞(|x| ≥ R) ≤ C||u||pτ·(|x| ≥ (1)/2R).

Abstract: In this paper, we get the L∞ estimate for the solutions of the following elliptic equation in RN with limiting Sobolev exponent and inhomogeneous term
-∑i=1N(∂)/∂xi(|▽u|p-2(∂u)/∂xi)+c(x)|u|p-2u=f(x,u)+g(x),u∈RN,u∈W1,p(RN),N > p > 1 and we show that any solution u of the above equation satisfies
||u||∞(|x| ≥ R) ≤ C||u||pτ·(|x| ≥ (1)/2R).

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