The raising steps method. Applications to the $\displaystyle L^{r}$ Hodge theory in a compact riemannian manifold.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T03:08:35Z | |
| dc.date.available | 2024-04-04T03:08:35Z | |
| dc.date.created | 2017-10 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193540 | |
| dc.description.abstractEn | 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 | |
| dc.language.iso | en | |
| dc.subject.en | Hodge Laplacian | |
| dc.subject.en | $L^r$ Hodge decomposition | |
| dc.subject.en | compact Riemannian manifold | |
| dc.title.en | The raising steps method. Applications to the $\displaystyle L^{r}$ Hodge theory in a compact riemannian manifold. | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1506.00418 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01158323 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01158323v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMAR,%20Eric&rft.genre=preprint |
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