Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/17304

Title: Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory
Authors: Garetto, Claudia
Keywords: Algebras of generalized functions
Fundamental solutions
Regularity theory
Issue Date: 2008
Publisher: © Springer-Verlag
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.
Abstract: 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.
Description: 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.
Sponsor: Research of C. Garetto was supported by FWF (Austria), grants T305-N13 and Y237-N13.
Version: Accepted for publication
DOI: 10.1007/s10440-008-9220-8
URI: https://dspace.lboro.ac.uk/2134/17304
Publisher Link: http://dx.doi.org/10.1007/s10440-008-9220-8
ISSN: 0167-8019
Appears in Collections:Published Articles (Maths)

Files associated with this item:

File Description SizeFormat
fund sol.pdfAccepted version349.23 kBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.