The diamagnetic inequality for the Dirichlet-to-Neumann operator
| hal.structure.identifier | University of Auckland [Auckland] | |
| dc.contributor.author | A.F.M. TER ELST, . | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:55:02Z | |
| dc.date.available | 2024-04-04T02:55:02Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192326 | |
| dc.description.abstractEn | Let Ω be a bounded domain in R d with Lipschitz boundary Γ. We define the Dirichlet-to-Neumann operator N on L 2 (Γ) associated with a second order elliptic operator A = − d k,j=1 ∂ k (c kl ∂ l) + d k=1 b k ∂ k − ∂ k (c k ·) + a 0. We prove a criterion for invariance of a closed convex set under the action of the semigroup of N. Roughly speaking, it says that if the semigroup generated by −A, endowed with Neumann boundary conditions, leaves invariant a closed convex set of L 2 (Ω), then the 'trace' of this convex set is invariant for the semigroup of N. We use this invariance to prove a criterion for the domination of semigroups of two Dirichlet-to-Neumann operators. We apply this criterion to prove the diamagnetic inequality for such operators on L 2 (Γ). | |
| dc.language.iso | en | |
| dc.subject.en | Dirichlet-to-Neumann operator | |
| dc.subject.en | invariance of convex sets | |
| dc.subject.en | domination of semi- groups | |
| dc.subject.en | diamagnetic inequality Home institutions: | |
| dc.title.en | The diamagnetic inequality for the Dirichlet-to-Neumann operator | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 2004.09782 | |
| 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-02547609 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02547609v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=A.F.M.%20TER%20ELST,%20.&OUHABAZ,%20El%20Maati&rft.genre=preprint |
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