A Lewy-Stampacchia inequality in variable Sobolev spaces for pseudomonotone operators

In this paper, we are interested in proving the Lewy-Stampacchia inequality in the general framework of an obstacle problem for a nonlinear pseudomonotone elliptic operator in W 1,p(·) 0 (Ω) where p(·) is a log-Holder continuous exponent. Our aim is to adapt to the context of variable exponent Sobolev spaces a previous work of the first author, based on a penalization method. Mathematics subject classification (2010): 35J85, 35R35.