Non-autonomous maximal regularity for fractional evolution equations

Maximal Regularity for Evolution Equations Governed by Non-Autonomous Forms

We consider a non-autonomous evolutionary problem u̇(t) + A(t)u(t) = f(t), u(0) = u0 where the operator A(t) : V → V ′ is associated with a form a(t, ., .) : V × V → R and u0 ∈ V . Our main concern is to prove well-posedness with maximal regularity which means the following. Given a Hilbert space H such that V is continuously and densely embedded into H and given f ∈ L(0, T ;H) we are interested...

Maximal Regularity for Evolution Equations

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

Maximal regularity for nonautonomous evolution equations

We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity. 1991 Mathematics Subject Classification. 35K90, 47D06.

Maximal L-regularity for Stochastic Evolution Equations

We prove maximal Lp-regularity for the stochastic evolution equation{ dU(t) +AU(t) dt = F (t, U(t)) dt+B(t, U(t)) dWH(t), t ∈ [0, T ], U(0) = u0, under the assumption that A is a sectorial operator with a bounded H∞calculus of angle less than 1 2 π on a space Lq(O, μ). The driving process WH is a cylindrical Brownian motion in an abstract Hilbert space H. For p ∈ (2,∞) and q ∈ [2,∞) and initial...