An improved setting for generalized functions: fine ultrafunctions
Analysis of PDEs
2022-03-14 v2
Abstract
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older definitions in many crucial points. Some applications are given to show how ultrafunctions can be applied in studing Partial Differential Equations. In particular, it is possible to prove the existence of ultrafunction solutions to ill posed evolution poblems.
Cite
@article{arxiv.2105.01490,
title = {An improved setting for generalized functions: fine ultrafunctions},
author = {Vieri Benci},
journal= {arXiv preprint arXiv:2105.01490},
year = {2022}
}