Open Access$L^{\Phi }-L^{\infty }$\ Inequalities and Applications
Author(s) -
Tiziano Granucci
Publication year - 2015
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v7n2p201
Subject(s) - nabla symbol , mathematics , omega , combinatorics , sobolev space , maxima and minima , scalar (mathematics) , sobolev inequality , prime (order theory) , mathematical analysis , geometry , physics , quantum mechanics
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.