English

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 RR\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.

Keywords

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

R2 v1 2026-06-23T02:44:48.767Z