Complete Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions, in UMD Spaces

Mustapha Cheggag , Angelo Favini , Rabah Labbas (1) , Stéphane Maingot (1) , Ahmed Medeghri

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

In this paper we prove some new results concerning a complete abstract second-order differential equation with general Robin boundary conditions. The study is developped in UMD spaces and uses the celebrated Dore-Venni Theorem. We prove existence, uniqueness and maximal regularity of the strict solution.

Mots clés: Abstract diff erential equations of second order; Boundary value problem of Robin type; UMD spaces; Bounded imaginary powers; Dore-Venni Theorem

Domaines: Equations aux dérivées partielles [math.AP]

Mustapha Cheggag, Angelo Favini, Rabah Labbas, Stéphane Maingot, Ahmed Medeghri. Complete Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions, in UMD Spaces. Discrete and Continuous Dynamical Systems - Series S, 2011, 4 (3), pp.523-538. ⟨hal-00971775⟩