TOPICS ON FUNCTIONAL ANALYSIS, CALCULUS OF VARIATIONS AND DUALITY

Key words and phrases. Banach spaces, convex analysis, duality, calculus of variations, non-convex systems, generalized method of lines Abstract. This work is a kind of revised and enlarged edition of the title Variational Convex Analysis, published by Lambert Academic Publishing. First we present the basic tools of analy-sis necessary to develop the core theory and applications. New results concerning duality principles for systems originally modeled by non-linear differential equations are shown in chapters 10 to 18. A key aspect of this work is that although the original problems are non-linear with corresponding non-convex variational formula-tions, the dual formulations obtained are almost always concave and amenable to numerical computations. When the primal prob-lem has no solution in the classical sense, the solution of dual prob-lem is a weak limit of minimizing sequences, and the evaluation of such average behavior is important in many practical applications