Sufficient conditions of local solvability for partial differential operators in the Colombeau context

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 G(Ω) as well as in the dual L(Gc(Ω), e C).