Can I read Lp-maximal Regularity for Non-autonomous Evolution Equations on EtoBox?

Lp-maximal Regularity for Non-autonomous Evolution Equations by Wolfgang Arendt; Ralph Chill; Simona Fornaro; César Poupaud is a Mathematics article available to read on EtoBox.

What is Lp-maximal Regularity for Non-autonomous Evolution Equations about?

Let A : [0, τ ] → L(D, X) be strongly measurable and bounded, where D, X are Banach spaces such that D → X. We assume that the operator A(t) has maximal regularity for all t ∈ [0, τ ]. Then we show under some additional hypothesis (viz. relative continuity) that the non-autonomous problem is well-posed in L p ; i.e. for all f ∈ L p (0, τ ; X) and all x ∈ (X, D) 1/p \* ,p there exists a unique u ∈ W 1,p (0, τ ; X) ∩ L p (0, τ ; D) solution of (P ), where 1 < p < ∞. If the operators A(t) are accretive, we show that conversely, well-posedness of (P ) implies that A(t) has maximal regularity for all t ∈ [0, τ ]. We also consider the non-autonomous second order problem for which we prove similar regularity and perturbation results.

Who reads Lp-maximal Regularity for Non-autonomous Evolution Equations?

Author

Wolfgang Arendt; Ralph Chill; Simona Fornaro; César Poupaud

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-0396)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)