$L^{\Phi }-L^{\infty }$\ Inequalities and Applications

In this paper we prove some $L^{\Phi }-L^{\Phi }$ and $L^{\Phi }-L^{\infty }$inequalities for quasi-minima of scalar integral functionals defined inOrlicz-Sobolev space $W^{1}L^{\Phi }\left( \Omega \right) $, where $\Phi $\is a N-function and $\Phi \in \triangle _{2}$. Moreover, if $\Phi \in\triangle ^{^{\prime }}$ or if $\Phi \in \triangle _{2}\cap \nabla _{2}$, weprove that quasi-minima are H\"{o}lder continuous functions.