Paper detail

Nonlocal elliptic problems with nonlinear argument transformations near the points of conjugation

We consider elliptic equations of order $2m$ in a domain $G\subset\mathbb R^n$ with nonlocal conditions that connect the values of the unknown function and its derivatives on $(n-1)$-dimensional submanifolds $Υ_i$ (where $\bigcup_iΥ_i=\partial G$) with the values on $ω_{is}(\overlineΥ_i)\subset\overline G$. Nonlocal elliptic problems in dihedral angles arise as model problems near the conjugation points $g\in\overlineΥ_i\capΥ_j\ne\varnothing$, $i\ne j$. We study the case where the transformations $ω_{is}$ correspond to nonlinear transformations in the model problems. It is proved that the operator of the problem remains Fredholm and its index does not change as we pass from linear argument transformations to nonlinear ones.