OUHABAZ, El Maati

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OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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Document de travail - Pré-publication

Resumen en inglés

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.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191555

Proyecto ANR

Analyse Réelle et Géométrie - ANR-18-CE40-0012

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Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251