Let
D
D
be a subdomain of a bounded domain
Ω
\Omega
in
R
n
{\mathbb {R}^n}
. The conductivity coefficient of
D
D
is a positive constant
k
≠
1
k \ne 1
and the conductivity of
Ω
∖
D
\Omega \backslash D
is equal to
1
1
. For a given current density
g
g
on
∂
Ω
\partial \Omega
, we compute the resulting potential
u
u
and denote by
f
f
the value of
u
u
on
∂
Ω
\partial \Omega
. The general inverse problem is to estimate the location of
D
D
from the known measurements of the voltage
f
f
. If
D
h
{D_h}
is a family of domains for which the Hausdorff distance
d
(
D
,
D
h
)
d(D,{D_h})
equal to
O
(
h
)
O(h)
(
h
h
small), then the corresponding measurements
f
h
{f_h}
are
O
(
h
)
O(h)
close to
f
f
. This paper is concerned with proving the inverse, that is,
d
(
D
,
D
h
)
≤
1
c
‖
f
h
−
f
‖
d(D,{D_h}) \leq \frac {1}{c}\left \| {f_h} - f\right \|
,
c
>
0
c > 0
; the domains
D
D
and
D
h
{D_h}
are assumed to be piecewise smooth. If
n
≥
3
n \geq 3
, we assume in proving the above result, that
D
h
⊃
D
{D_h} \supset D
(or
D
h
⊂
D
{D_h} \subset D
) for all small
h
h
. For
n
=
2
n = 2
this monotonicity condition is dropped, provided
g
g
is appropriately chosen. The above stability estimate provides quantitative information on the location of
D
h
{D_h}
by means of
f
h
{f_h}
.