Foundations of the calculus of variations in generalized function algebras

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dc.creatorKonjik, Sanja
dc.creatorKunzinger, Michael
dc.creatorOberguggenberger, Michael
dc.date2007-07-12
dc.date.accessioned2026-07-07T10:01:49Z
dc.date.available2026-07-07T10:01:49Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0707.1842
dc.identifierhttp://arxiv.org/abs/0707.1842
dc.identifierActa Appl. Math. 103: 169-199, 2008.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168758
dc.subjectFunctional Analysis
dc.subjectOptimization and Control
dc.subject49J27, 46F30, 49K27, 37K05
dc.titleFoundations of the calculus of variations in generalized function algebras
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