  We determine the conductivity of the interior of a body using electrical
measurements on its surface. We assume only that the conductivity is bounded
below by a positive constant and that the conductivity and surface are
Lipschitz continuous. To determine the conductivity we first solve an
associated integral equation locally, finding solutions in $H^1(B)$, where $B$
is a ball that properly contains the body. A key ingredient is to equip this
Sobolev space with an equivalent norm which depends on two auxiliary parameters
that can be chosen to yield a contraction.
