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The square root of a parabolic operator
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:46:29Z | |
| dc.date.available | 2024-04-04T02:46:29Z | |
| dc.date.created | 2020 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191555 | |
| dc.description.abstractEn | Let L(t) = −div (A(x, t)∇ x) for t ∈ (0, τ) be a uniformly elliptic operator with boundary conditions on a domain Ω of R d and ∂ = ∂ ∂t. Define the parabolic operator L = ∂ + L on L 2 (0, τ, L 2 (Ω)) by (Lu)(t) := ∂u(t) ∂t + L(t)u(t). We assume a very little of regularity for the boundary of Ω and assume that the coefficients A(x, t) are measurable in x and piecewise C α in t for some α > 1 2. We prove the Kato square root property for √ L and the estimate √ L u L 2 (0,τ,L 2 (Ω)) ≈ ∇ x u L 2 (0,τ,L 2 (Ω)) + u H 1 2 (0,τ,L 2 (Ω)) + τ 0 u(t) 2 L 2 (Ω) dt t 1/2. We also prove L p-versions of this result. Keywords: elliptic and parabolic operators, the Kato square root property, maximal regularity, the holomorphic functional calculus, non-autonomous evolution equations. | |
| dc.description.sponsorship | Analyse Réelle et Géométrie - ANR-18-CE40-0012 | |
| dc.language.iso | en | |
| dc.title.en | The square root of a parabolic 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 | 2006.10326 | |
| 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-02871224 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02871224v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=OUHABAZ,%20El%20Maati&rft.genre=preprint |
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