A Simplified Approach in the Study of Elliptic Differential Equations in UMD Spaces and New Applications

Angelo Favini , Rabah Labbas (1) , Stéphane Maingot (1) , Hiroki Tanabe , Atsushi Yagi

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

This paper is devoted to provide some new clarifications in the study of complete abstract second order differential equations of elliptic type given in our recent papers [8],[9] and [10]. We improve the situation in the case of the space L^{p}(0,1;X) with a UMD Banach space X by considering an approach generalizing those used in [10]. On the other hand, we give some new examples to which our theory applies.

Mots clés: Abstract differential equations of second order; Boundary value problem; UMD spaces; Bounded imaginary powers; Maximal regularity; Dore-Venni theorem.; Dore-Venni theorem

Domaines: Equations aux dérivées partielles [math.AP]

Angelo Favini, Rabah Labbas, Stéphane Maingot, Hiroki Tanabe, Atsushi Yagi. A Simplified Approach in the Study of Elliptic Differential Equations in UMD Spaces and New Applications. Funkcialaj ekvacioj.Serio internacia, 2008, 51, pp.165-187. ⟨hal-00995102⟩