Maximal regularity for second order non-autonomous Cauchy problems

Maximal Regularity of Discrete Second Order Cauchy Problems in Banach Spaces

We characterize the discrete maximal regularity for second order difference equations by means of spectral and R-boundedness properties of the resolvent set.

Non-autonomous Inhomogeneous Boundary Cauchy Problems

In this paper we prove existence and uniqueness of classical solutions for the non-autonomous inhomogeneous Cauchy problem d dt u(t) = A(t)u(t) + f(t), 0 ≤ s ≤ t ≤ T, L(t)u(t) = Φ(t)u(t) + g(t), 0 ≤ s ≤ t ≤ T, u(s) = x. The solution to this problem is obtained by a variation of constants formula.

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...

On maximal parabolic regularity for non-autonomous parabolic operators

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...

Semilinear Evolution Equations of Second Order via Maximal Regularity