English

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

Analysis of PDEs 2009-02-04 v1

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(\Om)\G(\Om) as well as in the dual \LL(\Gc(\Om),\wt\C)\LL(\Gc(\Om),\wt{\C}).

Keywords

Cite

@article{arxiv.0902.0508,
  title  = {Sufficient conditions of local solvability for partial differential operators in the Colombeau context},
  author = {Claudia Garetto},
  journal= {arXiv preprint arXiv:0902.0508},
  year   = {2009}
}