GARETTO, C., 2010. G- and G∞-hypoellipticity of partial differential operators with constant Colombeau coefficients. IN: Kaminski, A., Oberguggenberger, M. and Pilipovic, S. (eds). Linear and Non-Linear Theory of Generalized Functions and its Applications. IMPAN, pp. 111 - 131
Banach Center Publications;88
We provide a deep investigation of the notions of G- and G∞-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 G- and G∞-hypoellipticity are given.
This paper was published in the Banach Center Publication Series and is available here with the kind permission of the publisher.
Research of the author supported by FWF (Austria), grant T305-N13.