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
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