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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