Lions' maximal regularity problem with H12-regularity in time

On Maximal L-regularity

The aim of this paper is to propose weak assumptions to prove maximal L q regularity for Cauchy problem : du dt (t) − 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 pro...

A solution to the problem of Lp−maximal regularity

We give a negative solution to the problem of the Lp-maximal regularity on various classes of Banach spaces including Lq-spaces with 1 < q / = 2 < +∞. Mathematics Subject Classification (1991):47D06, 46B03, 46B52, 46C15

A Solution to the Problem of L−maximal Regularity

We give a negative solution to the problem of the L-maximal regularity on various classes of Banach spaces including L-spaces with 1 < q 6= 2 < +∞.

Maximal Regularity for Evolution Equations

Regularity in residuated lattices

In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in re...