Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (1): 41-46.

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ON VERY WEAK SOLUTIONS OF A-HARMONIC EQUATION WITH VERY WEAK BOUNDARY VALUES

 GAO Hong-Y, YE Yu-Quan, XIE Su-Ying   

  1. Department of Mathematics, Hebei University, Baoding 071002, China Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
  • Online:2002-01-14 Published:2002-01-14
  • Supported by:

    The research supported by National Natural Science Foundation of China.

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Abstract:

In this paper,the following result is given by using Hodge decomposition:There exists r0 = r0(n, p, a, b),such that if u 2 W1,rloc () is a very weak solution of (1.1),withmax{1, p−1} < r < p and u 2 W1,r0 (; @\E), where E  @ is a closed set and small inan appropriate capacity sense, then u = 0, a.e. in  provided that r0 < r < p.

Key words: A-harmonic equation, Very weak solution, Uniqueness, Hodge decomposi-tion

CLC Number: 

  • 35J65
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