Maximal regularity for second order non-autonomous Cauchy problems
Volume 189 / 2008
Studia Mathematica 189 (2008), 205-223
MSC: Primary 47E05; Secondary 34G10, 35B65, 47D09.
DOI: 10.4064/sm189-3-1
Abstract
We consider some non-autonomous second order Cauchy problems of the form We assume that the first order problem \dot u + B(t) u = f \quad (t\in [0,T]) , \ \quad u(0) =0, has L^p-maximal regularity. Then we establish L^p-maximal regularity of the second order problem in situations when the domains of B(t_1) and A(t_2) always coincide, or when A(t) = \kappa B(t).
