\(L^ p\) regularity for abstract differential equations. (English) Zbl 0818.47044

Dore, Giovanni

Komatsu, Hikosaburo (ed.), Functional analysis and related topics, 1991. Proceedings of the international conference in memory of Professor Kôsaku Yosida held at RIMS, Kyoto University, Japan, July 29-Aug. 2, 1991. Berlin: Springer-Verlag. Lect. Notes Math. 1540, 25-38 (1993).

The paper under review is a survey of results about \(L^ p\) regularity for a certain Cauchy problem for an abstract differential equation in a Banach space. The author restricts the discussion to autonomous equations. He concludes with three open problems concerning \(L^ p\) regularity for the above Cauchy problem.
For the entire collection see [Zbl 0782.00076].

Reviewer: H.Haruki (Waterloo / Ontario)

MSC:

47E05	General theory of ordinary differential operators
34G10	Linear differential equations in abstract spaces

Keywords:

Cauchy problem; abstract differential equation in a Banach space; autonomous equations; \(L^ p\) regularity