  Let $D$ be an bounded region in ${\bf R}^n$. The regularity of solutions of a
family of quasilinear elliptic partial differential equations is studied, one
example being $\Delta_nu=Vu^{n-1}$. The coefficients are assumed to be in the
space $L\log^{m}L(D)$ for $m>n-1$. Using a Moser iteration argument coupled
with the Moser-Trudinger inequality, a local $L^{\infty}$ bound on the solution
$u$ is proven. A Harnack-type inequality is then proven. These results are
shown to be sharp with respect to $m$. Then essential continuity of $u$ is
proven, and away from the boundary a bound on the modulus of continuity.
