On general Bitsadze–Samarskii problems of elliptic type in L^p cases

This paper is devoted to the study of General Bitsadze–Samarskii Problems of elliptic type in the framework of UMD Banach spaces. Here, we obtain some results about existence, uniqueness and regularity of the solution. We define two types of solutions (strict and semi-strict solutions) and we give necessary and sufficient conditions on the data to obtain these results.