A priori estimates for solutions of g-Laplace type problems

Abstract

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. 2000 Mathematics Subject Classification. 35J20; 35J60.