$L^{r}$ solutions of elliptic equation in a complete riemannian manifold.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T03:06:34Z | |
| dc.date.available | 2024-04-04T03:06:34Z | |
| dc.date.created | 2018 | |
| dc.date.issued | 2019 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193346 | |
| dc.description.abstractEn | Let $X$ be a complete metric space and $\Omega $ a domain in $ X.$ The Local Increasing Regularity Method (LIRM) allows to get from emph{local} a priori estimates on solutions $u$ of a linear equation $ Du=\omega $ \emph{global} ones in $ \Omega .$As an application we shall prove that if $D$ is an elliptic linear differential operator of order $m$ with ${\mathcal{C}}^{\infty }$ coefficients operating on $p$-forms in a compact Riemannian manifold $M$ without boundary and $\omega \in L^{r}_{p}(M)\cap (\mathrm{k}\mathrm{e}mathrm{r}D^{*})^{\perp },$ then there is a $u\in W^{m,r}_{p}(M)$ such that $Du=\omega $ on $M.$ Next we investigate the case of a compact manifold with boundary. In the last sections we study the case of a complete but non compact Riemannian manifold by use of adapted weights.\ | |
| dc.language.iso | en | |
| dc.title.en | $L^{r}$ solutions of elliptic equation in a complete riemannian manifold. | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal of Geometric Analysis | |
| bordeaux.page | 2565-2599 | |
| bordeaux.volume | 23 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01738700 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01738700v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Geometric%20Analysis&rft.date=2019&rft.volume=23&rft.issue=3&rft.spage=2565-2599&rft.epage=2565-2599&rft.au=AMAR,%20Eric&rft.genre=article |
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