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In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a ij(x)■ij u+b i(x)■iu+f(x,u)=0,in ΩRn,(*)where aij■iφ■jφ=0 on■Ω,andφis the defining function of ■Ω.Imposing suitable conditions on the coefficients and f(x,u)