Abstract
If
Au=−div(a(x,Du))
is a monotone operator defined on the Sobolev space
W
1,p
(
R
n
)
,
1<p<+∞
, with
a(x,0)=0
for a.e.
x∈
R
n
, the capacity
C
A
(E,F)
relative to
A
can be defined for every pair
(E,F)
of bounded sets in
R
n
with
E⊂F
. We prove that
C
A
(E,F)
is increasing and countably subadditive with respect to
E
and decreasing with respect to
F
. Moreover we investigate the continuity properties of
C
A
(E,F)
with respect to
E
and
F
.