Let
F
∈
W
loc
1
,
n
(
Ω
;
R
n
)
{F \in W_{{\text {loc}}}^{1,n}(\Omega ;{\mathbb {R}^n})}
be a mapping with nonnegative Jacobian
J
F
(
x
)
=
det
D
F
(
x
)
≥
0
{{J_F}(x) = \det DF(x) \geq 0}
for a.e. x in a domain
Ω
⊂
R
n
{\Omega \subset {\mathbb {R}^n}}
. The dilatation of F is defined (almost everywhere in
Ω
{\Omega }
) by the formula
\[
K
(
x
)
=
|
D
F
(
x
)
|
n
J
F
(
x
)
.
K(x) = \frac {{|DF(x){|^n}}}{{{J_F}(x)}}.
\]
Iwaniec and Šverák [IS] have conjectured that if
p
≥
n
−
1
{p \geq n - 1}
and
K
∈
L
l
o
c
p
(
Ω
)
{K \in L_{loc}^p(\Omega )}
then F must be continuous, discrete and open. Moreover, they have confirmed this conjecture in the two-dimensional case n = 2. In this article, we verify it in the higher-dimensional case
n
≥
2
{n \geq 2}
whenever
p
>
n
−
1
{p > n - 1}
.