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Original Articles

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

, , , &
Pages 1453-1475 | Received 13 May 2011, Accepted 24 Oct 2011, Published online: 28 Nov 2011
 

Abstract

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 Hölder 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 Hölder 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].

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Acknowledgements

The authors thank the referees for their useful comments and remarks.

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