- and $^{∞}$-hypoellipticity of partial differential operators with constant Colombeau coefficients

Claudia Garetto

- and

^{\infty}

-hypoellipticity of partial differential operators with constant Colombeau coefficients

Claudia Garetto

Banach Center Publications, Tome 89 (2010), p. 111-131 / Harvested from The Polish Digital Mathematics Library

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Résumé

We provide a deep investigation of the notions of - and $^{\infty}$ -hypoellipticity for partial differential operators with constant Colombeau coefficients. This involves generalized polynomials and fundamental solutions in the dual of a Colombeau algebra. Sufficient conditions and necessary conditions for - and $^{\infty}$ -hypoellipticity are given

Publié le : 2010-01-01

Zbl 1195.35117

EUDML-ID : urn:eudml:doc:281812

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     author = {Claudia Garetto},
     title = {- and $^{$\infty$}$-hypoellipticity of partial differential operators with constant Colombeau coefficients},
     journal = {Banach Center Publications},
     volume = {89},
     year = {2010},
     pages = {111-131},
     zbl = {1195.35117},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-9}
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Claudia Garetto. - and $^{∞}$-hypoellipticity of partial differential operators with constant Colombeau coefficients. Banach Center Publications, Tome 89 (2010) pp. 111-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-9/