Sufficient conditions of local solvability for partial differential operators in the Colombeau context

Claudia Garetto

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arXiv · 0902.0508

Sufficient conditions of local solvability for partial differential operators in the Colombeau context

Claudia Garetto

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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 $\G(\Om)$ as well as in the dual $\LL(\Gc(\Om),\wt{\C})$.

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Claudia Garetto. 2009-02-03. Sufficient conditions of local solvability for partial differential operators in the Colombeau context. https://arxiv.org/abs/0902.0508

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