1. Partial Differential Inequalities and Unilateral Problems (Variational Inequalities)
J. L. Lions · Society for Industrial and Applied Mathematics eBooks · 1972
1. Minimization of convex functionals. We recall here a number of well-known results in convex analysis. Let us consider a functionalv→J(v)defined on Uad⊂U and with values in ℝ; we suppose that:Uis a reflexive Banach space onℝ;(1.1.1)Uadis aclosed convexset inU;(1.1.2)JisconvexandcontinuousonUad.(1.1.3)