  In this work we study a priori bounds for weak solution to elliptic problems
with nonstandard growth that involves the so-called $g-$Laplace operator. The
$g-$Laplacian is a generalization of the $p-$Laplace operator that takes into
account different behaviors than pure powers. The method to obtain this a
priori estimates is the so called ``blow-up'' argument developed by Gidas and
Spruck. Then we applied this a priori bounds to show some existence results for
these problems.
