On the Fredholm and unique solvability of nonlocal elliptic problems in multidimensional domains

Abstract

We consider elliptic equations of order $2m$ in a bounded domain $Q\subset {\mathbb{R}}^n$ with nonlocal boundary-value conditions connecting the values of a solution and its derivatives on $(n-1)$-dimensional smooth manifolds ${\Gamma }_i$ with the values on manifolds ${\omega }_i({\Gamma }_i)$, where ${\bigcup }_i\overline{{\Gamma }_i}=\partial Q$ is a boundary of $Q$ and ${\omega }_i$ are $C^{\infty }$ diffeomorphisms. By proving a priori estimates for solutions and constructing a right regularizer, we show the Fredholm solvability in weighted space. For nonlocal elliptic problems with a parameter, we prove the unique solvability.

63 pages, 5 figures

References in corpus (3)

• Solvability of nonlocal elliptic problems in Sobolev spaces
• Nonlocal problems for elliptic equations in dihedral angles and the Green formula
• Smoothness of generalized solutions for nonlocal elliptic problems on the plane

Cited by in corpus (1)

• On the existence of a Feller semigroup with atomic measure in nonlocal boundary condition