Evolutionary problems driven by variational inequalities with multiple integral functionals

Abstract

In this paper, the authors focus on extending the well-known weak sharp solutions for variational inequalities to a controlled variational-type inequality governed by convex multiple integral functionals. Simultaneously, some equivalent conditions on weak sharpness associated with solutions of the considered inequality are obtained by using the minimum principle sufficiency property.

Keywords

• controlled variational-type inequality
• weak sharp solution
• convex multiple integral functional
• minimum principle sufficiency property
• dual gap functional