Abstract
The existence of continuous linear right inverses for partial differential equations is proved in certain weighted spaces of C ∞-functions and distributions. Continuity estimates are given for the right inverses. This makes the problem accessible to a perturbation argument and may be used to prove the existence of right inverses for certain partial differential operators with C ∞-coefficients, which are ”constant at ∞”. These right inverses satisfy the same continuity estimates as in the case of constant coefficients. The main tools are the *-tame splitting of the ∂∂-complex and the *-tame sequence space representations and splitting theory of D. Vogt for power series spaces of infinite type.
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© 1989 Kluwer Academic Publishers
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Langenbruch, M. (1989). Tame Right Inverses for Partial Differential Equations. In: Terzioñlu, T. (eds) Advances in the Theory of Fréchet Spaces. NATO ASI Series, vol 287. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2456-7_7
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DOI: https://doi.org/10.1007/978-94-009-2456-7_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7608-1
Online ISBN: 978-94-009-2456-7
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