$\mathcal G$- 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
