Solvability of nonlocal elliptic problems in weight spaces

Abstract

In this paper we consider elliptic equations of order 2m in a bounded domainQ є Rn with boundaryδQ and nonlocal conditions relating the traces of the solution and its derivatives on (n − 1)-dimensional smooth manifolds Γi (∪i =∂δQ) to their values on some compact setF ⊂Q, whereF ∩δQ ≠ Φ. The Fredholm solvability of these problems in the weight spacesVp, a/l+2m(Q) is proved for arbitrary 1<p <∞.