Complete Abstract Differential Equations of Elliptic Type in UMD Spaces

Angelo Favini; Rabah Labbas; Stéphane Maingot; Hiroki Tanabe; Atsushi Yagi

doi:10.1619/fesi.49.193

Angelo Favini, Rabah Labbas, Stéphane Maingot, Hiroki Tanabe, Atsushi Yagi

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Keywords: Abstract differential equations of second order, Boundary conditions, UMD spaces, Bounded imaginary powers, Maximal regularity, Dore-Venni theorem

JOURNAL FREE ACCESS

2006 Volume 49 Issue 2 Pages 193-214

DOI https://doi.org/10.1619/fesi.49.193

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Abstract

In this paper we give new results on complete abstract second order differential equations of elliptic type in UMD Banach spaces. Existence, uniqueness and maximal regularity of the strict solution are proved using the celebrated Dore-Venni Theorem. This work completes the ones studied in the framework of Hölder spaces, see [7] and [8].

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