In this talk, we consider elliptic equations of the following type $$ -mathrm{div},left(a(x)|Du|^{p-2}Du ight)+ V|u|^{p-2}u=-mathrm{div},left(|F|^{p-2}F ight) ext{in} Omega, u=0 ext{on} partialOmega. $$ Here $V$ is nonnegative function. For $gamma>frac{n}{p}$, we prove that if $Vin L^q(Omega)$ satisfies the reverse H"older inequality that $$ left(frac{1}{|B|}int_BV^{gamma}dx ight)^{frac{1}{gamma}}leq cfrac{1}{|B|}int_BVdx $$ for all balls $B$ and for some constant $c>0$, then the following implication holds $$ Fin L^q(Omega) Longrightarrow Fin L^q(Omega) $$ for every $qleq gamma^*(p-1)$ with $gamma^*:=frac{ngamma}{n-gamma}$, under possibly minimal assumptions on coefficients and domains.