  The Hausdorff dimension of general Sierpinski carpets, [4] and [20], and the
generalization on Lalley-Gatzouras carpets, [10], are today well known results,
the formulas being obtain via the variational principle for the dimension. We
call the multidimensional versions of these carpets Sierpinski sponges and
self-affine sponges, respectively,. In this paper we show that the Hausdorff
dimension of self-affine sponges, defined in R3, is a Lipschitz continuous
function at Sierpinski sponges.
