Sturm–Liouville problems in weighted spaces in domains with non-smooth edges. II
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URI (для ссылок/цитирований):
https://link.springer.com/article/10.3103%2FS1055134416040027https://elib.sfu-kras.ru/handle/2311/69835
Автор:
Шлапунов, Александр Анатольевич
Tarkhanov, Nikolai
Коллективный автор:
Институт математики и фундаментальной информатики
Кафедра теории функций
Дата:
2016-10Журнал:
Siberian Advances in mathematicsКвартиль журнала в Scopus:
Q4Библиографическое описание:
Шлапунов, Александр Анатольевич. Sturm–Liouville problems in weighted spaces in domains with non-smooth edges. II [Текст] / Александр Анатольевич Шлапунов, Nikolai Tarkhanov // Siberian Advances in mathematics. — 2016. — Т. 26 (№ 4). — С. 247-293Аннотация:
We consider a (generally, noncoercive) mixed boundary value problem in a bounded domain D of Rn for a second order elliptic differential operator A(x, ∂). The differential operator is assumed to be of divergent form in D and the boundary operator B(x, ∂) is of Robin type on ∂D. The boundary of D is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset Y ⊂ ∂D and control the growth of solutions near Y. We prove that the pair (A, B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set Y. Moreover, we prove the completeness of root functions related to L