Acta mathematica scientia,Series B

• Articles •     Next Articles

THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS

 DIAO Dun-Ning, CENG Xiao-Meng   

  • Online:2005-10-11 Published:2005-10-11
  • Supported by:

    The project was supported by NSFC(19971070)

Abstract:

In this paper,  the first boundary value problem for quasilinear
equation of the form
$$\Delta A(u, \ x)+\sum_{i=1}^{m}\frac{\partial b^{i}(u, \ x)}{\partial x_{i}}
+c(u, \ x)=0, \ \ \ \ \ \ \ \ A_{u}(u, \ x)\geq 0
 $$
is studied. By using the compensated compactness theory, some results on the existence of weak
solution are established. In addition, under certain condition the uniqueness of
solution is proved.

Key words: Dirichlet problem;degenerate elliptic equation, existence of solutions

CLC Number: 

  • 35J25
Trendmd