It is shown that a
k
k
-cell (the homeomorphic image of a closed ball in
R
k
\mathbb {R}^{k}
) in
R
n
\mathbb {R}^{n}
,
1
≤
k
>
n
1\leq k>n
, cannot support a function in
W
1
,
p
(
R
n
)
W^{1,p}(\mathbb {R}^{n})
if
p
>
[
k
+
1
2
]
p>[\frac {k+1}{2}]
, the greatest integer in
(
k
+
1
)
/
2
(k+1)/2
.