  Let $\Omega \subset {\mathbb R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and
$\delta$ be the distance to $\partial \Omega$. We study positive solutions of
equation (E) $-L_\mu u+ g(|\nabla u|) = 0$ in $\Omega$ where $L_\mu=\Delta +
\frac{\mu}{\delta^2} $, $\mu \in (0,\frac{1}{4}]$ and $g$ is a continuous,
nondecreasing function on ${\mathbb R}_+$. We prove that if $g$ satisfies a
singular integral condition then there exists a unique solution of (E) with a
prescribed boundary datum $\nu$. When $g(t)=t^q$ with $q \in (1,2)$, we show
that equation (E) admits a critical exponent $q_\mu$ (depending only on $N$ and
$\mu$). In the subcritical case, namely $1<q<q_\mu$, we establish some a priori
estimates and provide a description of solutions with an isolated singularity
on $\partial \Omega$. In the supercritical case, i.e. $q_\mu\leq q<2$, we
demonstrate a removability result in terms of Bessel capacities.
