Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type

Garetto, Claudia

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Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type

journal contribution

posted on 2015-04-20, 10:24 authored by Claudia Garetto

We provide sufficient conditions of local solvability for partial differential operators with variable Colombeau coefficients. We mainly concentrate on operators which admit a right generalized pseudodifferential parametrix and on operators which are a bounded perturbation of a differential operator with constant Colombeau coefficients. The local solutions are intended in the Colombeau algebra G(Ω) as well as in the dual L(G c(Ω), ℂ̃). © 2009 Texas State University - San Marcos.

Funding

Author was supported by grant T305-N13 from FWF, Austria.

History

School

Science

Department

Mathematical Sciences

Published in

Electronic Journal of Differential Equations

Volume

2009

Pages

1 - 43

Citation

GARETTO, C., 2009. Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type. Electronic Journal of Differential Equations, 116, pp. 1 - 43.

Publisher

Version

VoR (Version of Record)

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

2009

Notes

This article was published in the Electronic Journal of Differential Equations [© Texas State University]. It is also available at: http://ejde.math.txstate.edu/Volumes/2009/116/garetto.pdf