  We study local boundedness for subsolutions of nonlinear nonuniformly
elliptic equations whose prototype is given by $\nabla \cdot (\lambda |\nabla
u|^{p-2}\nabla u)=0$, where the variable coefficient $0\leq\lambda$ and its
inverse $\lambda^{-1}$ are allowed to be unbounded. Assuming certain
integrability conditions on $\lambda$ and $\lambda^{-1}$ depending on $p$ and
the dimension, we show local boundedness. Moreover, we provide counterexamples
to regularity showing that the integrability conditions are optimal for every
$p>1$.
