Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces
Angelo Favini, Rabah Labbas, Stéphane Maingot, Hiroki Tanabe, Atsushi Yagi · Discrete and Continuous Dynamical Systems · 2008
In this paper we give new results on complete abstract second order differential equations of elliptic type in the framework of Hölder spaces, extending those given in [4] and [5]. More precisely we study $u^{\prime \prime }+2Bu^{\prime }+Au=f$ in the case when $f$ is Hölder continuous and under some natural assumptions on the operators $A$ and $B$. We give necessary and sufficient conditions of compatibility to obtain a strict solution $u$ and also to ensure that the strict solution has the maximal regularity property.