The Lions-Magenes type theorems for Lawruk elliptic boundary-value problems

Abstract

We investigate elliptic boundary-value problems with additional unknown functions in boundary-conditions introduced by Lawruk. We prove that these problems are Fredholm in some Sobolev spaces of order $s<2q$, where $2q$ is the order of the corresponding elliptic equation. Thus, we establish certain versions of the Lions-Magenes theorems for these problems.