A priori bounds for a class of semi-linear degenerate elliptic equations

In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\label{000} a^{ij}(x)\partial_{ij}u+b^i(x)\partial_i u +f(x,u)=0,$\text{in}$\Omega\subset\subset R^n, {equation} where $a^{ij}\partial_i \phi\partial_j \phi=0$on$\partial \Omega$,$\phi$isthedefiningfunctionof$\partial \Omega$\mathrm{.}Imposingsuitableconditionsonthecoefficientsand$f(x,u)$,onecangetthe$L^\infty$-estimates of \eqref{000} via blow up method.