The raising steps method. Applications to the $\displaystyle L^{r}$ Hodge theory in a compact riemannian manifold.
Résumé
Let $X$ be a complete metric space and $\displaystyle \Omega
$ a domain in $\displaystyle X.$ The Raising Steps Method allows
to get from local results on solutions $u$ of a linear equation
$\displaystyle Du=\omega $ global ones in $\displaystyle \Omega .$\ \par
It was introduced in~\cite{AmarSt13} to get good estimates on
solutions of $\bar \partial $ equation in domains in a Stein manifold.\ \par
As a simple application we shall get a strong $\displaystyle
L^{r}$ Hodge decomposition theorem for $p-$forms in a compact
riemannian manifold without boundary, and then we retrieve this
known result by an entirely different and simpler method.\ \par
Origine : Fichiers produits par l'(les) auteur(s)
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