Lewy-Stampacchia inequality for noncoercive parabolic obstacle problems

Abstract

We investigate the obstacle problem for a class of nonlinear and noncoercive parabolic variational inequalities whose model is a Leray–Lions type operator having singularities in the coefficients of the lower order terms. We prove the existence of a solution to the obstacle problem satisfying a Lewy-Stampacchia type inequality.

Keywords

• noncoercive evolution problems
• obstacle problems
• penalization
• lewy–stampacchia inequality
• marcinkiewicz spaces