Non-autonomous maximal regularity in weighted space

Mahdi Achache (1) , Tebbani Hossni

1 IMB - Institut de Mathématiques de Bordeaux

We consider the problem of maximal regularity for non-autonomous Cauchy problems u ′ (t) + A(t)u(t) = f (t) (t ∈ [0, τ ]), u(0) = u 0. The time dependent operators A(t) are associated with sesquilinear forms on a Hilbert space H. We prove the maximal regularity in the weighted space L 2 (0, τ, t β dt; H), with β ∈] − 1, 1[ and we prove also other regularity properties for the solution of the previous problem. Our result is motivated by boundary value problems.

Mots clés: Maximal regularity; non-autonomous evolution equations; weighted space

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Mahdi Achache, Tebbani Hossni. Non-autonomous maximal regularity in weighted space. 2018. ⟨hal-01822281⟩