Generalized solutions of variational problems and applications

Advances in Nonlinear Analysis

article

Vieri Benci¹  Lorenzo Luperi Baglini³  Marco Squassina⁴ 

[1] Dipartimento di Matematica, Università degli Studi di Pisa;Centro Linceo interdisciplinare Beniamino Segre;Faculty of Mathematics, University of Vienna;Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore

关键词: Ultrafunctions;    non-Archimedean mathematics;    nonstandard analysis;    delta function;   

DOI  :  10.1515/anona-2018-0146

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ * ⊃ ℝ {\mathbb{R}^{*}\supset\mathbb{R}} that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions and we study the relationships between these generalized solutions and classical minimizing sequences. Finally, we study some examples to highlight the potential of this approach.

【 授权许可】

CC BY