On Maximal L^p-regularity

Details On Maximal L^p-regularity On Maximal L^p-regularity

2009-02-16

arxiv.org/abs/0902.2691v1

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

The aim of this paper is to propose weak assumptions to prove maximal L^q regularity for Cauchy problem: du/dt - Lu(t)=f(t). Mainly we only require "off-diagonal" estimates on the real semigroup (e^{tL})_{t>0} to obtain maximal L^q regularity. The main idea is to use a one kind of Hardy space H^1 adapted to this problem and then use interpolation results. These techniques permit us to prove weighted maximal regularity too.

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