Linear functionals on nonlinear spaces and applications to problems from viscoplasticity theory

A classical result in the theory of monotone operators states that if C is a reflexive Banach space, and an operator A: C(right arrow)C* is monotone, semicontinuous and coercive, then A is surjective. In this paper, we define the "dual space" C* of a convex, usually not linear, subset C of some Banach space X (in general, we will have C*(superset of)X*) and prove an analogous result. Then, we give an application to problems from viscoplasticity theory, where the natural space to look for solutions is not linear.