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$\mathcal G$- and $\mathcal{G}^{\infty}$-hypoellipticity of partial differential operators with constant Colombeau coefficients

Volume 88 / 2010

Banach Center Publications 88 (2010), 111-131 MSC: Primary 46F30; Secondary 35H99. DOI: 10.4064/bc88-0-9

Abstract

We provide a deep investigation of the notions of $\mathcal{G}$- and $\mathcal{G}^\infty$-hypoellipticity for partial differential operators with constant Colombeau coefficients. This involves generalized polynomials and fundamental solutions in the dual of a Colombeau algebra. Sufficient conditions and necessary conditions for $\mathcal{G}$- and $\mathcal{G}^\infty$-hypoellipticity are given

Authors

• Claudia GarettoInstitut für Grundlagen der Bauingenieurwissenschaften
Leopold-Franzens-Universität Innsbruck
Technikerstr. 13
A 6020 Innsbruck, Austria
e-mail

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