Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory Claudia Garetto 2134/17304 https://repository.lboro.ac.uk/articles/journal_contribution/Fundamental_solutions_in_the_Colombeau_framework_applications_to_solvability_and_regularity_theory/9385196 In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual ℒ(Gc(ℝ n), ℂ∼). After having proved the existence of a fundamental solution for a large class of partial differential operators with constant Colombeau coefficients, we investigate the relationships between fundamental solutions in ℒ(Gc(ℝn), ℂ∼), Colombeau solvability and G- and G∞ -hypoellipticity respectively. © 2008 Springer Science+Business Media B.V. 2015-04-17 14:58:20 Algebras of generalized functions Fundamental solutions Regularity theory Mathematical Sciences not elsewhere classified