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Let $\Omega$ be a bounded open set in $\mathbb{R}^n$ and $u\in H^1(\Omega)\cap L^{\infty}(\Omega)$ be the weak subsolution of the following nonlinear and heterogeneous elliptic equation: $-\nabla\cdot(|\nabla u|^{p-2}\nabla u)+c(x)|u|^{p-2}u=f$ where $0\le c(x)\le M$ and $f\in L^\infty(\Omega)$. That is, for every $\phi\in H^1(\Omega)\cap L^{\infty}(\Omega)$, $\int_\Omega|\nabla u|^{p-2}\nabla u\cdot\nabla\phi+c(x)|u|^{p-2}u\phi\,dx\le\int_\Omega f\phi\,dx$

Show that there exists a constant $R_0=R_0(M)>0$, such that for every $0 and $\forall x_0\in\Omega$, $$\sup_{B_{\frac{R}{2}}}u\le C\left(\frac{1}{R^n}\int_{B_R}u^p\,dx\right)^{\frac{1}{p}}+C\|f\|_\infty,$$ where $B_R=B_R(x_0)\subset\Omega$ and $C=C(n,R_0,M)$.

I think this can be done by a generalized version of Moser iteration, extended from linear case to nonlinear one. Can anyone give some clues or references? Thank you~

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    Probably you can find good ideas in this paper: http://www.mai.liu.se/~toada/harnack_final.pdf2012-07-14

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