MR2271232 Favini, Angelo, Labbas, Rabah, Maingot, Stéphane, Tanabe, Hiroki and Yagi, Atsushi Angelo FAVINI, Rabah LABBAS, Stéphane MAINGOT, Hiroki TANABE and Atsushi YAGI Complete Abstract Differential Equations of Elliptic Type in UMD Spaces Funkcialaj Ekvacioj. Serio Internacia 49 2006 193--214 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-2/49_193.pdf http://www.ams.org/mathscinet-getitem?mr=MR2271232 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]. Abstract differential equations of second order, Boundary conditions, UMD spaces, Bounded imaginary powers, Maximal regularity, Dore-Venni theorem. 35J25, 35J40, 47D06. 49-193 2006 Complete Abstract Differential Equations of Elliptic Type in UMD Spaces FAVINI, Angelo, LABBAS, Rabah, MAINGOT, Stéphane, TANABE, Hiroki and YAGI, Atsushi Angelo FAVINI, Rabah LABBAS, Stéphane MAINGOT, Hiroki TANABE and Atsushi YAGI
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