fund sol.pdf (349.23 kB)
Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory
journal contribution
posted on 2015-04-17, 14:58 authored by Claudia GarettoIn 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 MathematicaeVolume
102Issue
2-3Pages
281 - 318Citation
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-VerlagVersion
- 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
2008Notes
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
0167-8019eISSN
1572-9036Publisher version
Language
- en