The raising steps method. Applications to the $\bar \partial $ equation in Stein manifolds.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T02:20:23Z | |
| dc.date.available | 2024-04-04T02:20:23Z | |
| dc.date.created | 2013-12 | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 1050-6926 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189484 | |
| dc.description.abstractEn | In order to get estimates on the solutions of the equation $\bar \partial u=\omega $ on Stein manifold, we introduce a new method the "raising steps method", to get global results from local ones. In particular it allows us to transfer results form open sets in ${\mathbb{C}}^{n}$ to open sets in a Stein manifold.\ \par Using it we get $\displaystyle L^{r}-L^{s}$ results for solutions of equation $\bar \partial u=\omega $ with a gain, $\displaystyle s>r,$ in strictly pseudo convex domains in Stein manifolds.\ \par We also get $\displaystyle L^{r}-L^{s}$ results for domains in ${\mathbb{C}}^{n}$ locally biholomorphic to convex domains of finite type. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | The raising steps method. Applications to the $\bar \partial $ equation in Stein manifolds. | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1312.7648 | |
| bordeaux.journal | The Journal of Geometric Analysis | |
| bordeaux.page | 898-913 | |
| bordeaux.volume | 26 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00922689 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00922689v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=The%20Journal%20of%20Geometric%20Analysis&rft.date=2016&rft.volume=26&rft.issue=2&rft.spage=898-913&rft.epage=898-913&rft.eissn=1050-6926&rft.issn=1050-6926&rft.au=AMAR,%20Eric&rft.genre=article |
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