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
as well as in the dual
.
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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