On Parabolic Variational Inequalities with Multivalued Terms and Convex Functionals

Abstract

In this paper, we consider the following parabolic variational inequality containing a multivalued term and a convex functional: Find u∈Lp⁢(0,T;W01,p⁢(Ω)){u\in L^{p}(0,T;W^{1,p}_{0}(\Omega))} and f∈F⁢(⋅,⋅,u){f\in F(\cdot,\cdot,u)} such that u⁢(⋅,0)=u0{u(\cdot,0)=u_{0}} and

Keywords

• variational inequalities
• multivalued term
• convex functional
• sub-supersolutions
• extremal solutions
• 58e35
• 47j20
• 47j25
• 35j87