The classical theory of calculus of variations for generalized functions

Advances in Nonlinear Analysis

article

Alexander Lecke¹  Lorenzo Luperi Baglini²  Paolo Giordano² 

[1] Universität Wien;Wolfgang Pauli Institute, Universität Wien

关键词: Calculus of variations;    Schwartz distributions;    generalized functions for nonlinear analysis;    low regular Riemannian geometry;   

DOI  :  10.1515/anona-2017-0150

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY