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Mosc. Math. J., 2009, Volume 9, Number 4, Pages 899–926 (Mi mmj370)  

This article is cited in 3 scientific papers (total in 3 papers)

On the Hodge decomposition in $\mathbb R^n$

Marc Troyanov

Section de Mathématiques, École Polytechnique Féderale de Lausanne, Lausanne, Switzerland

Abstract: We prove a version of $L^p$-Hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. Using these tools, we also compute $L_{q,p}$-cohomology of $\mathbb R^n$.

Key words and phrases: Hodge decomposition, temperate currents, Lizorkin currents.

DOI: https://doi.org/10.17323/1609-4514-2009-9-4-899-926

Full text: http://www.ams.org/.../abst9-4-2009.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 58A10, 42B, 42B20, 58A14
Received: January 11, 2008
Language:

Citation: Marc Troyanov, “On the Hodge decomposition in $\mathbb R^n$”, Mosc. Math. J., 9:4 (2009), 899–926

Citation in format AMSBIB
\Bibitem{Tro09}
\by Marc~Troyanov
\paper On the Hodge decomposition in $\mathbb R^n$
\jour Mosc. Math.~J.
\yr 2009
\vol 9
\issue 4
\pages 899--926
\mathnet{http://mi.mathnet.ru/mmj370}
\crossref{https://doi.org/10.17323/1609-4514-2009-9-4-899-926}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2663996}
\zmath{https://zbmath.org/?q=an:05692632}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000273089600009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gol'dshtein V., Troyanov M., “The Holder-Poincaré duality for L-q,L-p-cohomology”, Ann Global Anal Geom, 41:1 (2012), 25–45  crossref  mathscinet  zmath  isi  scopus
    2. Jacobs H., Vankerschaver J., “Fluid-Structure Interaction in the Lagrange-Poincaré Formalism: the Navier–Stokes and Inviscid Regimes”, J. Geom. Mech., 6:1 (2014), 39–66  crossref  mathscinet  zmath  isi  scopus
    3. Mazzeo R., Pelayo A., Ratiu T.S., “l-2-Cohomology and Complete Hamiltonian Manifolds”, J. Geom. Phys., 87 (2015), 305–313  crossref  mathscinet  zmath  isi  scopus
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