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

الأصل · EN

We consider elliptic equations of order 2m in a bounded domain Qⁿ with nonlocal boundary-value conditions connecting the values of a solution and its derivatives on (n-1)-dimensional smooth manifolds Γᵢ with the values on manifolds ωᵢ(Γᵢ), where ᵢΓᵢ=∂ Q is a boundary of Q and ωᵢ are C∞ 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.