Electron. J. Diff. Equ., Vol. 2009(2009), No. 116, pp. 1-43.

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

Claudia Garetto

Abstract:
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 $\mathcal{G}(\Omega)$ as well as in the dual $\mathcal{L}(\mathcal{G}_c(\Omega),\widetilde{\mathbb{C}})$.

Submitted June 22, 2009. Published September 21, 2009.
Math Subject Classifications: 46F30, 35D99.
Key Words: Algebras of generalized functions; generalized solutions of partial differential equations.

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Claudia Garetto
Institut für Grundlagen der Bauingenieurwissenschaften
Leopold-Franzens Universität Innsbruck
Technikerstrasse 13, 6020 Innsbruck, Austria
email: claudia@mat1.uibk.ac.at

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