Elliptic problems with Robin boundary coefficient-operator conditions in general $L_p$ Sobolev spaces and applications

In this paper we prove some new results on complete operational second order differential equations of elliptic type with coefficient-operator conditions, in the framework of the space $L^{p}(0,1; X)$ with general $p\in (1,+\infty)$, $X$ being a UMD Banach space. Existence, uniqueness and optimal regularity of the classical solution are proved. This paper improves and completes naturally our last two works on this problematic.