  We investigate the asymptotic behaviour of entropy and approximation numbers
of the compact embedding $E^m_{p,\sigma}(B)\hookrightarrow L_p(B)$, $1\leq
p<\infty,$ defined on the unit ball $B$ in $\mathbb{R}^n$. Here
$E^m_{p,\sigma}(B)$ denotes a Sobolev space with a power weight perturbed by a
logarithmic function. The weight contains a singularity at the origin. Inspired
by Evans and Harris, we apply a bracketing technique which is an analogue to
that of Dirichlet-Neumann-bracketing used by Triebel if $p=2$.
