New results on abstract elliptic problems with general Robin boundary conditions in Hölder spaces: non commutative cases

Rabah Labbas (1) , Rabah Haoua (2) , Stéphane Maingot (1) , Ahmed Medeghri (2)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées

In this paper, we prove some new results on operational second order differential equations of elliptic type with general Robin boundary conditions in a non-commutative framework. The study is developed in Hölder spaces under some natural assumptions generalizing those in [4]. We give necessary and sufficient conditions on the data to obtain a unique strict solution satisfying the maximal regularity property, see Theorems 1 and 2. This work completes the one given in [4] and [12].

Mots clés: Second-order elliptic differential equations; Robin boundary conditions; Analytic semigroup

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Rabah Labbas, Rabah Haoua, Stéphane Maingot, Ahmed Medeghri. New results on abstract elliptic problems with general Robin boundary conditions in Hölder spaces: non commutative cases. Bollettino dell'Unione Matematica Italiana, 2022, ⟨10.1007/s40574-021-00311-7⟩. ⟨hal-03513265⟩