An obstacle problem via a sequence of penalized problems

Abstract:

In this paper, we shall concern with the existence result of unilateral parabolic degenerated problems associated to the equations of the form

where A is a classical Leray-Lions operator acting from the weighted Sobolev space into its dual L^p′ (0, T, W^-1,p′ (Ω, w*)), while the datum f is assumed in L¹(Q_T).

The proof is based on the penalty methods.