Generalized solutions of variational problems and applications
Functional Analysis
2018-06-29 v1 Analysis of PDEs
Abstract
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field 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.
Cite
@article{arxiv.1806.10953,
title = {Generalized solutions of variational problems and applications},
author = {Vieri Benci and Lorenzo Luperi Baglini and Marco Squassina},
journal= {arXiv preprint arXiv:1806.10953},
year = {2018}
}
Comments
23 pages. arXiv admin note: text overlap with arXiv:1707.09265