Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type Claudia Garetto 2134/17308 https://repository.lboro.ac.uk/articles/journal_contribution/Sufficient_conditions_of_local_solvability_for_partial_differential_operators_on_spaces_of_colombeau_type/9388229 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 G(Ω) as well as in the dual L(G c(Ω), ℂ̃). © 2009 Texas State University - San Marcos. 2015-04-20 10:24:53 Algebras of generalized functions Generalized solutions of partial differential equations Mathematical Sciences not elsewhere classified