Let \(G\) be a bounded domain in \(E^ n\) and \(p>1\). Consider the following elliptic equation \[ \int_ G\{\nabla v\cdot A(x,u,\nabla u)+vB(x,u,\nabla u)\}dx=0,\quad\forall v\in{\overset\circ W^ 1_ p}(G)\cap L_ \infty(G), \tag{1} \] where \(A(x,u,\xi)\) and \(B(x,u,\xi)\) are defined on \(G\times E^ 1\times E^ n\), continuous in \(u\) and \(\xi\) for fixed \(x\) and measurable in \(x\) for fixed \(u\) and \(\xi\), respectively. Moreover, suppose \(A\) and \(B\) satisfy: \[ \begin{aligned}\nabla u\cdot A(x,u,\nabla u) & \;\geq\;|\nabla u|^ p-K| u|^ q-f_ 0(x),\\ | A(x,u,\nabla u)| & \;\leq \;K_ 1|\nabla u|^{p-1}+K| u|^{q/p'}+f_ 1(x),\\ | B(x,u,\nabla u)| & \;\leq \;C(x)|\nabla u|^ \gamma+K| u|^{q- 1}+f_ 2(x), \end{aligned}\tag{2} \] where \(1n/(p- \gamma)\) as \(\gamma>p-1\), \(f_ i(x)\in L_{S_ i}(G)\) \((i=0,1,2)\), \(S_ 0\), \(S_ 2>n/p\) and \(S_ 1>n/(p-1)\). Now let \(t=n(\gamma+1-p)/(p-\gamma)\) as \(r=\infty\); \(t=nr(\gamma+1- p)/(r(p-\gamma)-n)\) as \(n/(p-\gamma)0\) such that \(\text{mes} B(x_ 0,\rho)\backslash G\geq \theta \text{mes} B(x_ 0,\rho)\), \(\forall x_ 0\in\partial G\), \(\rho\leq R\) is fulfilled, then the solution \(u\in{\overset\circ W^ 1_ p}(G)\cap L_ t(G)\) of the equation (1) is globally bounded on \(G\) and uniformly Hölder continuous on \(G\).