Data di Pubblicazione:
2019
Citazione:
The classical theory of calculus of variations for generalized functions / A. Lecke, L. Luperi Baglini, P. Giordano. - In: ADVANCES IN NONLINEAR ANALYSIS. - ISSN 2191-9496. - 8:1(2019), pp. 779-808. [10.1515/anona-2017-0150]
Abstract:
We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove full connections between extremals and Euler-Lagrange equations, classical necessary and sufficient conditions to have a minimizer, the necessary Legendre condition, Jacobi's theorem on conjugate points and Noether's theorem. We close with an application to low regularity Riemannian geometry.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Calculus of variations; Schwartz distributions; generalized functions for nonlinear analysis; low regular Riemannian geometry
Elenco autori:
A. Lecke, L. Luperi Baglini, P. Giordano
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