Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions
| dc.contributor.author | TER ELST, A.F.M. | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:56:31Z | |
| dc.date.available | 2024-04-04T02:56:31Z | |
| dc.date.issued | 2019-03 | |
| dc.identifier.issn | 1424-3199 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192471 | |
| dc.description.abstractEn | Let Ω be a bounded open subset with C 1+κ-boundary for some κ > 0. Consider the Dirichlet-to-Neumann operator associated to the elliptic operator − ∂ l (c kl ∂ k) + V , where the c kl = c lk are Hölder continuous and V ∈ L ∞ (Ω) are real valued. We prove that the Dirichlet-to-Neumann operator generates a C 0-semigroup on the space C(∂Ω) which is in addition holomorphic with angle π 2. We also show that the kernel of the semigroup has Poisson bounds on the complex right half-plane. As a consequence we obtain an optimal holomorphic functional calculus and maximal regularity on L p (Γ) for all p ∈ (1, ∞). | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | C 0 -semigroup | |
| dc.subject.en | Poisson bounds | |
| dc.subject.en | holomorphic semigroup Home institutions: | |
| dc.subject.en | AMS Subject Classification: 47D06 | |
| dc.subject.en | 35K08 Keywords: Dirichlet-to-Neumann operator | |
| dc.title.en | Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00028-018-0467-x | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Journal of Evolution Equations | |
| bordeaux.page | 21-31 | |
| bordeaux.volume | 19 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02486374 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02486374v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Evolution%20Equations&rft.date=2019-03&rft.volume=19&rft.issue=1&rft.spage=21-31&rft.epage=21-31&rft.eissn=1424-3199&rft.issn=1424-3199&rft.au=TER%20ELST,%20A.F.M.&OUHABAZ,%20El%20Maati&rft.genre=article |
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