Abstract differential equations of elliptic type with general Robin boundary conditions in Hoelder spaces

In this article, we prove some new results on abstract second-order differential equations of elliptic type with general Robin boundary conditions. The study is performed in Holder spaces and uses the well-known Da Prato-Grisvard sum theory. We give necessary and sufficient conditions on the data to obtain a unique strict solution satisfying the maximal regularity property. This work completes the ones studied by Favini et al. [A. Favini, R. Labbas, S. Maingot, H. Tanabe, and A. Yagi, Necessary and sufficient conditions in the study of maximal regularity of elliptic differential equations in Holder spaces, Discrete Contin. Dyn. Syst. 22 (2008), pp. 973-987] and Cheggag et al. [M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri, Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces, Differ. Int. Eqns 21(9-10) (2008), pp. 981-1000].