Necessary and sufficient conditions for the solvability and maximal regularity of abstract differential equations of mixed type in UMD spaces

Abstract

In this paper we give some results on some abstract second order differential elliptic equations with mixed type boundary conditions. The study is performed in UMD spaces. The main purpose of this paper is the study of necessary and sufficient conditions on the data for obtaining existence, uniqueness and maximal regulariy properties of the strict solution. On the other hand, we give some new examples related to traces results.