Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 116, pp. 1-43.

Title: Sufficient conditions of local solvability for partial
       differential operators on spaces of Colombeau type

Author: Claudia Garetto (Leopold-Franzens Univ., Innsbruck, Austria)

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 $\mathcal{G}(\Omega)$ as well as in the dual
 $\mathcal{L}(\mathcal{G}_c(\Omega),\widetilde{\mathbb{C}})$.

Submitted June 22, 2009. Published September 21, 2009.
Math Subject Classifications: 46F30, 35D99.
Key Words: Algebras of generalized functions;
 generalized solutions of partial differential equations.