Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces. (25th March 2015) - Dong, Ge; Fang, Xiaochun
Abstract : We consider the existence of solutions of variational inequality form. Findu ∈ 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, whereA is a second-order elliptic operator of Leray-Lions type, F is a multivalued lower order term, andJ is a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces.