Dirichlet-to-Neumann and elliptic operators on C 1+κ -domains: Poisson and Gaussian bounds
| hal.structure.identifier | University of Auckland [Auckland] | |
| dc.contributor.author | TER ELST, A.F.M. | |
| hal.structure.identifier | Université de Bordeaux [UB] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T03:10:06Z | |
| dc.date.available | 2024-04-04T03:10:06Z | |
| dc.date.created | 2017 | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193661 | |
| dc.description.abstractEn | We prove Poisson upper bounds for the heat kernel of the Dirichlet-to-Neumann operator with variable Hölder coefficients when the underlying domain is bounded and has a C 1+κ-boundary for some κ > 0. We also prove a number of other results such as gradient estimates for heat kernels and Green functions G of elliptic operators with possibly complex-valued coefficients. We establish Hölder continuity of ∇ x ∇ y G up to the boundary. These results are used to prove L p-estimates for commutators of Dirichlet-to-Neumann operators on the boundary of C 1+κ-domains. Such estimates are the keystone in our approach for the Poisson bounds. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | 58G11 | |
| dc.subject.en | AMS Subject Classification: 35K08 | |
| dc.subject.en | 47B47 | |
| dc.subject.en | Keywords: Dirichlet-to-Neumann operator | |
| dc.subject.en | Poisson bounds | |
| dc.subject.en | elliptic operators with com- | |
| dc.subject.en | plex coefficients | |
| dc.subject.en | heat kernel bounds | |
| dc.subject.en | gradient estimates for Green functions | |
| dc.subject.en | commutator | |
| dc.subject.en | estimates | |
| dc.subject.en | Home institutions: | |
| dc.title.en | Dirichlet-to-Neumann and elliptic operators on C 1+κ -domains: Poisson and Gaussian bounds | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1705.10158 | |
| bordeaux.journal | Journal of Differential Equations | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01528301 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01528301v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2019&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=TER%20ELST,%20A.F.M.&OUHABAZ,%20El%20Maati&rft.genre=article |
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