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Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory

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journal contribution
posted on 2015-04-17, 14:58 authored by Claudia Garetto
In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual ℒ(Gc(ℝ n), ℂ∼). After having proved the existence of a fundamental solution for a large class of partial differential operators with constant Colombeau coefficients, we investigate the relationships between fundamental solutions in ℒ(Gc(ℝn), ℂ∼), Colombeau solvability and G- and G∞ -hypoellipticity respectively. © 2008 Springer Science+Business Media B.V.

Funding

Research of C. Garetto was supported by FWF (Austria), grants T305-N13 and Y237-N13.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Acta Applicandae Mathematicae

Volume

102

Issue

2-3

Pages

281 - 318

Citation

GARETTO, C., 2008. Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory. Acta Applicandae Mathematicae, 102 (2-3), pp. 281 - 318.

Publisher

© Springer-Verlag

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2008

Notes

This article was published in the journal, Acta Applicandae Mathematicae [© Springer-Verlag]. The final publication is available at Springer via http://dx.doi.org/10.1007/s10440-008-9220-8.

ISSN

0167-8019

eISSN

1572-9036

Language

  • en

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