This paper is devoted to the proof Gauss' divegence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently by Benci in 2013 and developed by the authors. Their peculiarity is that they are based on a non-Archimedean field, namely on a field which contains infinite and infinitesimal numbers. Ultra functions have been introduced to provide generalized solutions to equations which do not have any solutions, not even among the distributions.
A generalization of Gauss’ divergence theorem / V. Benci, L. Baglini (CONTEMPORARY MATHEMATICS). - In: Recent Advances in Partial Differential Equations and Applications / [a cura di] V.D. Radulescu, A. Sequeira, V.A. Solonnikov. - Prima edizione. - [s.l] : American Mathematical Society, 2016. - ISBN 9781470415211. - pp. 69-84 (( convegno International conference in honor of Hugo Beirao de Veiga's 70th birthday : February 17-21 tenutosi a Levico (TN Italy) nel 2014.
A generalization of Gauss’ divergence theorem
L. BagliniUltimo
2016
Abstract
This paper is devoted to the proof Gauss' divegence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently by Benci in 2013 and developed by the authors. Their peculiarity is that they are based on a non-Archimedean field, namely on a field which contains infinite and infinitesimal numbers. Ultra functions have been introduced to provide generalized solutions to equations which do not have any solutions, not even among the distributions.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Benci_Luperi_x_HUGO_15.pdf
accesso riservato
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
416.61 kB
Formato
Adobe PDF
|
416.61 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
