Colombeau generalized functions and solvability of differential operators

Details Colombeau generalized functions and solvability of differential operators Colombeau generalized functions and solvability of differential operators

2006-03-24

arxiv.org/abs/math/0603586v1

Zeitschrift f\"ur Analysis und ihre Anwendungen (ZAA), vol. 25: 4, p. 467-477, (2006)

Mathematics

Functional Analysis

Scientific paper

The aim of this paper is to prove that the well known non solvable Mizohata
type partial differential equations have Colombeau generalized solutions which
are distributions if and only if they are solv- able in the space of Schwartz
distributions. Therefore the Colombeau generalized solvability includes both a
new solution concept and new mathematical objects as solutions.

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