Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory

Claudia Garetto

Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory

Analysis of PDEs 2007-05-23 v2

Authors: Claudia Garetto

Abstract

In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual $\LL(\Gc(\R^n),\wt{\C})$ . 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 $\LL(\Gc(\R^n),\wt{\C})$ , Colombeau solvability and $\G$ - and $\Ginf$ -hypoellipticity respectively.

Cite

@article{arxiv.math/0701344,
  title  = {Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory},
  author = {Claudia Garetto},
  journal= {arXiv preprint arXiv:math/0701344},
  year   = {2007}
}

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