Non-autonomous maximal regularity under Besov regularity in time

Mahdi Achache (1)

1 IMB - Institut de Mathématiques de Bordeaux

We consider the maximal regularity problem for the non-autonomous Cauchy problems u ′ (t) + A(t)u(t) = f (t) t-a.e., u(0) = u 0. (0.1) In this case, the time dependent operators A(t) are associated with a family of sesquilinear forms. We prove maximal L p-regularity results with p ≤ 2 under minimal regularity assumptions on the forms. Our main assumption is that (A(t)) t∈[0,τ ] are piecewise in the Besov space B 1 2 ,2 p with respect to the variable t. This regularity assumption is optimal and our result is the most general one.

Mots clés: Besov space; maximal regularity; mon-autonomous evolution equations; sesquilinear forms. Mathematics Subject Classification (2010): 35K90; 35K45; 47D06

Domaines: Mathématiques [math]

Mahdi Achache. Non-autonomous maximal regularity under Besov regularity in time. 2021. ⟨hal-03104494⟩