Maximal Regularity for Nonautonomous Evolution Equations

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 Regularity for Evolution Equations

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

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...

Maximal regularity for evolution equations in weighted Lp - spaces

LetX be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem u̇(t)+ Au(t) = f (t), t > 0, u(0) = 0, enjoys maximal regularity in weighted Lp-spaces with weights ω(t) = tp(1−μ), where 1/p < μ, if and only if it has the property of maximal Lp-regularity. Moreover, it is also shown that the derivation operator D = d/dt admits anH∞-calculus in weigh...