Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory
Claudia Garetto
Abstract
In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual ((n),). 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 ((n),), Colombeau solvability and - and -hypoellipticity respectively.
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