2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168758We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we introduce the first and second variation of a variational problem. We then derive necessary (Euler-Lagrange equations) and sufficient conditions for extremals. The concept of association is used to obtain connections to a distributional description of singular variational problems. We study variational symmetries and derive an appropriate version of Nöther's theorem. Finally, a number of applications to geometry, mechanics, elastostatics and elastodynamics are presented.Functional AnalysisOptimization and Control49J27, 46F30, 49K27, 37K05text