Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces

Abstract EN

We consider the existence of solutions of variational inequality form.

Find u ∈ D ( J ) : 〈 A ( u ) , v - u 〉 + 〈 F ( u ) , v - u 〉 + J ( v ) - J ( u ) ≥ 0 , ∀ v ∈ W 1 L M ( Ω ) , whose principal part is having a growth not necessarily of polynomial type, where A is a second-order elliptic operator of Leray-Lions type, F is a multivalued lower order term, and J is a convex functional.

We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces.