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This article is cited in 7 scientific papers (total in 7 papers)
Non-local elliptic problems with non-linear argument transformations near the points of conjugation
P. L. Gurevich
Abstract:
We consider elliptic equations of order $2m$ in a domain $G\subset\mathbb R^n$ with non-local conditions that connect the values of the unknown function and its derivatives on
$(n-1)$-dimensional submanifolds $\overline\Upsilon_i$ (where
$\bigcup_i\overline\Upsilon_i=\partial G$ with the values on
$\omega_{is}(\overline\Upsilon_i)\subset\overline G$. Non-local elliptic problems in dihedral angles arise as model problems near the conjugation points
$g\in\overline\Upsilon_i\cap \overline\Upsilon_j\ne\varnothing$, $i\ne j$. We study the case when the transformations $\omega_{is}$ correspond to non-linear 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 non-linear ones.
Received: 15.03.2002
Citation:
P. L. Gurevich, “Non-local elliptic problems with non-linear argument transformations near the points of conjugation”, Izv. Math., 67:6 (2003), 1149–1186
Linking options:
https://www.mathnet.ru/eng/im460https://doi.org/10.1070/IM2003v067n06ABEH000460 https://www.mathnet.ru/eng/im/v67/i6/p71
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